UFL/COEL2001/0 I/
MODELING THE EFFECTS OF HYDRODYNAMICS, SUSPENDED
SEDIMENTS, AND WATER QUALITY ON LIGHT
ATTENTUATION IN INDIAN RIVER LAGOON, FLORIDA
by
DAVID JOSEPH CHRISTIAN
THESIS
2001
Coastal & Oceanographic Engineering Program
Department of Civil & Coastal Engineering
433 Weil Hall *P.O. Box 116590 Gainesville, Florida 326116590
UNIVERSITY OF
FLORIDA
UFL/COEL2001/017
MODELING THE EFFECTS OF HYDRODYNAMICS, SUSPENDED
SEDIMENTS, AND WATER QUALITY ON LIGHT
ATTENTUATION IN INDIAN RIVER LAGOON, FLORIDA
by
DAVID JOSEPH CHRISTIAN
THESIS
2001
MODELING THE EFFECTS OF HYDRODYNAMICS,
SUSPENDED SEDIMENTS, AND WATER QUALITY ON LIGHT ATTENUATION
IN INDIAN RIVER LAGOON, FLORIDA
By
DAVID JOSEPH CHRISTIAN
A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
UNIVERSITY OF FLORIDA
2001
Copyright 2001
by
David Joseph Christian
I dedicate this thesis to my family, whose love and support have helped me get to where I
am.
ACKNOWLEDGMENTS
I would like to thank the chairman of my committee, Dr. Peter Sheng, for his support
and guidance throughout my master's study. I would also like to thank the other members
of my committee, Dr. Robert Dean and Dr. Edward Phlips, for their help and insight.
The St. Johns River Water Management District funded the IRLPLR (Indian River
Lagoon Pollutant Load Reduction) model development project, which provided me the
opportunity to study light attenuation processes in the IRL. I need to extend a special thank
you to Justin Davis, Haifang Du, Detong Sun, Chenxia Qiu, and all of Dr. Sheng's other
students for their help and friendship. I am also indebted to Adam Kornick who started the
light attenuation work. I also cannot thank Dr. Chuck Gallegos enough for providing
information on his model and answering my long list of questions. A big thank you goes out
to the crew at the coastal lab, Sidney, Vik, Vernon, Chuck, and J. J., for helping with field
and lab work and being understanding when we brought something back from the field
broken. I would also like to thank Terry Johnson for helping with my diving.
Finally, I need to thank Kim Christmas for her friendship, support, and love. I could
not have made it without her.
TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS ............................................... iv
LIST OFTABLES ..................................................... ix
LISTOFFIGURES ............................................... xv
ABSTRACT ......................................................... xxi
1 INTRODUCTION AND BACKGROUND .............................. 1
1.1 Introduction and Background .......................................... 1
1.2 Light Definitions .................................................... 6
1.3 Seagrass and PAR Relationships ....................................... 13
1.4 Previous Light Attenuation M odels .................................... 15
1.5 This Study ..................... ............................... 18
2 DATA SETS ...................................................... 20
2.1 Introduction .................................................... ... 20
2.2 Sampling Procedures ............................................. .. 20
2.2.1 SERC Data Set ............................................. 20
2.2.2 UF Data Set ............................................... 22
2.2.3 WQMN Data ............................................ .. 25
2.2.4 HBOI Data ................................................. 25
2.2.5 Phlips Data ................................................. 27
2.3 Data Set Statistics .................................................. 28
2.3.1 SERC Data Set ..................................... ....... 28
2.3.2 UF Data Set ............................................ 29
2.3.3 WQMNDataSet ........................................... 30
2.3.4 HBOI Data Set ........................................... 31
2.3.5 Phlips Data Set .................................... ..........33
2.3.6 All Data Sets Comparison ..................................... 33
v
2.4 The Relative Importance of Various Factors for Light Attenuation ............. 34
2.4.1 Equations Used to Calculate Kd(PAR) Attributable to Each Variable .... 35
2.4.2 Data Set Analysis ........................................... 36
2.4.3 Percentage of Each Measured K/PAR) Due to Each Variable ......... 37
2.4.4 Analysis by Section .........................................42
2.4.5 Analysis by Season ......................................... 43
2.5 Data Differences ................................................... 45
2.5.1 UFData .................................................. 46
2.5.2 WQMN Data .............................................. 47
2.5.3 HBOIData ................................................ 51
2.5.4 Attempt to Make TSS Data Uniform ............................55
2.6 Data Sets Statistics With Converted TSS Values ........................... 57
2.6.1 Converted TSS Data Sets ..................................... 57
2.6.2 Season's Statistics ................ ......................... 58
2.6.3 Section's Statistics .......................................... 59
3 REGRESSION MODELS ............................................ 64
3.1 Introduction ...................................... ........... ... . 64
3.2 Regression Model Statistics ................ ......................... 66
3.3 Regression Models for Various Data Sets .............................. 69
3.3.1 Best OneVariable Linear Regression Model for Each Data Set ........ 69
3.3.2 Best TwoVariable Linear Regression Model for Each Data Set ....... 71
3.3.3 Best ThreeVariable Linear Regression Model for Each Data Set ...... 72
3.3.4 Best Three Variable Factorial Regression Model for Each Data Set ..... 76
3.4 Best Regression Models for Seasonal Data Sets ............................ 77
3.4.1 Best OneVariable Linear Regression Model for Each Season ......... 77
3.4.2 Best TwoVariable Linear Regression Model for Each Season ......... 80
3.4.3 Best ThreeVariable Linear Regression Model for Each Season ........ 81
3.4.4 Best ThreeVariable Factorial Regression Model for Each Season ...... 82
3.5 Best Regression Models for Each Section of the IRL ........................ 83
3.5.1 Best OneVariable Linear Regression Models for Each Section ........ 83
3.5.2 Best TwoVariable Linear Regression Model for Each Section ........ 85
3.5.3 Best ThreeVariable Linear Regression Model for Each Section ....... 87
3.5.4 Best ThreeVariable Factorial Regression Model for Each Section ..... 88
3.6 Summary of Regression Models ........................................ 89
4 NUMERICAL MODEL ........................................... 91
4.1 Introduction ........................... .......................... 91
4.2 Kirk's W ork ................................ ..................... 91
4.3 Gallegos's W ork .... ............................. ................. 93
4.3.1 Absorption by Water ...................................... 94
4.3.2
4.3.3
4.3.4
4.3.5
4.3.6
4.3.7
4.4 PARPS
Absorption by Yellow Substance ...........
Absorption by Phytoplankton .............
Absorption by Detritus ...................
Scattering by Particles ...................
Use of Absorption and Scattering Coefficients
Gallegos's Calibration for Use in the IRL ....
M odel ..............................
..... 94
..... 96
.....96
.....97
..... 98
.... 100
.... 102
5 NUMERICAL MODEL OF LIGHT ATTENUATION ......
5.1 Introduction ...................................................... 105
5.2 Debugging ........................................................106
5.3 Individual Data Set Runs ................ .......................... 106
5.3.1 Full Collected Data Sets ..................................... 107
5.3.2 Data Sets by Season ................ ....................... 116
5.3.3 Data Sets of Sections ........................................ 117
5.4 Alternate Model Coefficients ................ ....................... 120
5.4.1 Each Season's Coefficients .................................. 128
5.4.2 Each Section's Coefficients ............... ................. .132
5.4.3 Comparison of Monte Carlo Coefficients to Experimental Coefficients 140
5.5 Alternate TSSTurbidity Relationships
.. . . . . . . . . . . . . .. . 14 0
6 INTEGRATED MODEL RESULTS ................................
6.1 Introduction ...................................................
6.2 Model Architecture ..............................................
6.2.1 Allparpsworkch3d.f ....................................
6.2.2 Light Calculations .......................................
6.3 Segment Analysis ......................... .......................
6.3.1 Com prison to Data ......................................
6.3.2 Time Series Analysis .....................................
7 CONCLUSIONS ................ ......
.......................... 174
7.1 D ata Sets ....................
7.2 Individual Light Attenuation Models
7.3 Integrated Light Attenuation Model
7.4 Future W ork ..................
APPENDIX A ....................
APPENDIX B .............................. ........................ 187
..145
..145
..146
..147
..156
..157
..158
.... 174
.... 175
.... 177
.... 178
111 1111
111 111
A PPEN D IX C ........................................................ 190
LIST OFREFERENCES ................................................ 203
BIOGRAPHICAL SKETCH ............................................ 207
LIST OF TABLES
Table Page
2.1. Sample sites used in the SERC study. ................................ 21
2.2. SERC water quality variables used in the light attenuation model ........... 22
2.3. UF synoptic sampling trips were carried out on these dates ................ 23
2.4. UF water quality variables used in the light attenuation model. ............. 23
2.5. Sample sites used during UF synoptic sampling trips. ..................... 24
2.6. Additional sampling sites used during UF sampling trips 16 ............... 25
2.7. Sites sampled during WQMN sampling trips ........................... 26
2.8. HBOI water quality variables used in the light attenuation model ........... 27
2.9. Sample sites used during the HBOI study............................... 27
2.10. Data set statistics for the data collected during the SERC study. ............ 28
2.11. Statistics for the data collected during UF synoptic sampling
trips 16......................................................... 29
2.12. Statistics for the data collected during UF synoptic sampling trips 712 without
transformed TSS. ............................................... 30
2.13. Data set statistics for data collected by WQMN from March 1996
through 1998. .................................................. 31
2.14. Data set statistics for data collected by WQMN between March and May 1999
without transformed TSS. .................................... ..... 31
2.15. Data set statistics for HBOI data collected during HBOI's first sampling year
without transformed TSS. ..................................... 32
2.16. Data set statistics for HBOI data collected during HBOI's second sampling
year without transformed TSS. ..................................... 32
2.17. Data set statistics for data collected by Phlips during their October 1999
sampling trip in which TSS data were collected ........................ 33
2.18. Mean values of variables of interest from each of the data sets used in this
study without transformed TSS data .................................. 34
2.19. Percent of Kd(PAR) due to each attenuator in this study. .................. 37
2.20. Percentage of KdPAR) due to color, chlorophyll a, and tripton for each
data set for KdPAR) values above and below 1.00 m1 ..................... 40
2.21. Percentage of KdPAR) due to color, chlorophyll a, and tripton for each data
set for KdPAR) values above and below the mean KdPAR) value for each
data set. ................... ................................. ... 41
2.22. Percent of KdPAR) due to color, chlorophyll a, and tripton for each
section of the IRL. .................................... ............ 43
2.23. Percent of KdPAR) due to color, chlorophyll a, and tripton for
each season. ..................................................... 44
2.24. Turbidity calculations using HBOI years 1 and 2 average TSS values ........ 54
2.25. KdPAR) calculations using HBOI years 1 and 2 average TSS values. ........ 54
2.26. Results from TSS split sample analysis. ............................. .56
2.27. Transformed TSS statistics using WQMN 19941998 and WQMN 1999
turbidityTSS relationships. .......... .............................. 58
2.28. TSS statistics for data transformed using WQMN 19941998 and WQMN
1999 turbidityTSS relationships. .................................... 59
2.29. Statistics for January March with transformed TSS values. ............... 60
2.30. Statistics for April June with transformed TSS. ......................... 61
2.31. Statistics for July September with transformed TSS. .................... 61
2.32. Statistics for October December with transformed TSS.................... 61
2.33. Statistics for the South Section of the IRL with transformed TSS ........... 62
2.34. Statistics for the Middle Section of the IRL with transformed TSS .......... 62
2.35. Statistics for the North Section of the IRL with transformed TSS ............ 62
2.36. Statistics for the Banana River with transformed TSS .................... 63
2.37. Statistics for the Mosquito Lagoon with transformed TSS ................. 63
3.1. Best onevariable regression model for each data set ..................... 70
3.2. F values and p values for the best onevariable regression models. ......... 71
3.3. Best twovariable model for each data set. .......................... . 72
3.4. F values andp values for the best twovariable regression models. .......... 73
3.5. Best threevariable regression model for each data set ..................... 74
3.6. R2 values for the best threevariable model for each data set and the
improvement in R2 over the two variable model. ........................ 74
3.7. F values and p values for each variable in threevariable regression models.
.................................................... .......... .75
3.8. R2 values for the best threevariable factorial model for each data set
and the R2 improvement over the best threevariable regression model for each
data set. ...................................................... .76
3.9. Best threevariable factorial model for each data set. ...................... 78
3.10. Best onevariable model for each season. .............................. 79
3.11. F values and p values for each season's best onevariable model. ........... 80
3.12. Best twovariable model for each season. .............................. 80
3.13. F values andp values for each season's best two variable model. ........... 81
3.14. Best three variable model for each season. .................. ........ . 81
3.15. R2 for the best three variable regression model for each season and the R2
improvement over the best two variable models. ........................ 82
3.16. F values and p values for each season's best three variable regression model. .. 82
3.17. R2 for the three variable factorial model for each season and the R2
improvement over the three variable regression models.................... 83
3.18. Best three variable factorial model for each season ....................... 84
3.19. Best onevariable regression model for each section. ...................... 85
3.20. F values and p values for the best onevariable regression model for
each section. .................................................... 85
3.21. Best twovariable regression model for each section. ...................... 86
3.22. F values and p values for the best twovariable model for each section........ 86
3.23. Best threevariable regression model for each section. ..................... 87
3.24. R2 for the best threevariable regression model for each section and the R2
improvement over the best twovariable model for each section ............ 87
3.25. F values and p values for the best threevariable regression model for each
section. .............................................. ........... 88
3.26. R2 for each section's best threevariable factorial model and the R2
improvement over the best threevariable regression model for each section. .. 89
3.27. Best threevariable factorial model for each section ...................... 90
4.1. Absorption by water per wavelength. ................................ 95
4.2. Absorption by chlorophyll per wavelength. .................. ...... .. 97
4.3. Spectral incident PAR values. ............................... ....... 100
4.4. Gallegos's model coefficients for the Marker 198 sample site ............. 101
4.5. Gallegos's model coefficients for the Ft. Pierce Inlet sample site. .......... 101
4.6. Kornick's model coefficients for the entire IRL. ................... ..... 104
5.1. RMS errors (m1) of Kd(PAR) for numerical model runs using Marker 198
coefficients and Ft. Pierce coefficients .............................. 107
5.2. Mean Standard Deviation (m'1) from model results and data for each
data set. ....................................................... 108
5.3. RMS errors (m') for numerical model runs for each season using Marker 198
coefficients and Ft. Pierce coefficients. .............................. 116
5.4. Mean Standard Deviation (mi') from model results and data for
each season ................................................... 117
5.5. RMS errors (m') of Kd(PAR) for numerical model runs for each section
using Marker 198 coefficients and Ft. Pierce coefficients. ................ 120
5.6. Mean and Standard Deviation (m1) of Kd(PAR) from model results and data
for each section ................... ........................ .... 121
5.7. Coefficient ranges for use in Monte Carlo model ....................... 125
5.8. Results for SERC One Thousand Run Monte Carlo Tests With Sy = 0.016. ... 126
5.9. Comparison of RMS errors for each data set using Ft. Pierce coefficients and
SERC monte carlo coefficients with Sy = 0.0160 ........................ 127
5.10. Comparison of means standard deviations (mn') for KdPAR) from data,
model results with Ft. Pierce coefficients, and SERC monte carlo coefficients
with sy = 0.0160 ................... ....................... ....... 128
5.11. Coefficients for each of the seasons found by Monte Carlo method. ........ 133
5.12. Comparison of RMS errors of Kd(PAR) for model runs for each season
using the coefficients found by monte carlo method for each season,
coefficients found by monte carlo method for the SERC set, and the
Ft. Pierce coefficients (m1). .................. ............. ....... 133
5.13. Comparison of mean and standard deviation of modeled KdPAR) values for
each season using the coefficient set determined for the SERC data set with
the monte carlo method, the Ft. Pierce coefficient set, and data (mn) ........ 133
5.14. Coefficients found for each section by monte carlo method................ 137
5.15. Comparison of RMS errors for model runs for each section using the
coefficients found by monte carlo method for each section, coefficients
found by monte carlo method for the SERC set, and the Ft. Pierce
coefficients (m'). .............................................. 137
5.16. Comparison of mean and standard deviation of modeled KdPAR) values
for each section using the coefficient set determined for the SERC data set
with the monte carlo method, the Ft. Pierce coefficient set, and data (m'). ... 137
5.17. Comparison of RMS Error Values for the Northern IRL Data of Each Data Set
using Gallegos's Turbidity TSS Equation and the Turbidity TSS Equation
Found by Using WQMN 1996 1998 Sites 102, 107, and 110. ............. 144
6.1. Comparison of simulated results to modeled data for Segment 2 ........... 159
6.2. Comparison of simulated results to measured data for Segment 4 .......... 159
6.3. Comparison of simulated results and measured data for Segment 5. ........ 160
6.4. Comparison of simulated results and measured data for Segment 6. ........ 160
7.1. Comparison of model fits to data for a three variable stepwise model, three
variable factorial model, and PARPS numerical model for each collected
data set. ....................................................... 176
7.2. Comparison of model fits to data for a three variable stepwise model, three
variable factorial model, and PARPS numerical model for each season of
the year ............................................ .......... 177
7.3. Comparison of model fits to data for a three variable stepwise model, three
variable factorial model, and PARPS numerical model for each section of the
lagoon ....................................................... 177
A.1. Minimum, maximum, and mean values used for the model sensitivity tests. .. 180
C. 1. The Kd(PAR) (m1) values calculated for each grid layer (with 4 being the top
layer), the average value of the layer Kd(PAR)s, and the Kd(PAR) value calculated
using the entire water column for times during a one year, 1998 simulation for
Site ..........................................................193
C.2. The Kd(PAR) (m') values calculated for each grid layer (with 4 being the top
layer), the average value of the layer Kd(PAR)s, and the Kd(PAR) value calculated
using the entire water column for times during a one year, 1998 simulation for
Site 2. .........................................................194
C.3. The Kd(PAR) (m') values calculated for each grid layer (with 4 being the top
layer), the average value of the layer Kd(PAR)s, and the Kd(PAR) value calculated
using the entire water column for times during a one year, 1998 simulation for
Site3. ..........................................................195
C.4. The Kd(PAR) (m1) values calculated for each grid layer (with 4 being the top
layer), the average value of the layer Kd(PAR)s, and the Kd(PAR) value calculated
using the entire water column for times during a one year, 1998 simulation for
Site 4. .........................................................196
C.5. The Kd(PAR) (m1) values calculated for each grid layer (with 4 being the top
layer), the average value of the layer Kd(PAR)s, and the Kd(PAR) value calculated
using the entire water column for times during a one year, 1998 simulation for
Site 5...........................................................197
LIST OF FIGURES
Figure Page
1.1. Halodule wrightii ................................................. 3
1.2. Syringodiumfiliforme .............................................3
1.3. Halophila englemanii .............................................. 4
1.4. Thalassia testudinum ........................................... .4
1.5. Halophilajohnsonii and Halophila decipiens ............................ 5
1.6. Ruppia maritima ..................................... .......... .5
1.7. The setup for a detector measuring radiance through an angle A. .......... 8
1.8. A 27t PAR sensor for measuring downward irradiance .................... 10
1.9. A 47t PAR sensor for measuring downward irradiance ..................... 11
2.1. Percentage of Kd(PAR) due to chlorophyll a. ........................... 38
2.2. Percentage of Kd(PAR) due to color. ................................. 38
2.3. Percentage of Kd(PAR) due to tripton. ............................... 39
2.4. UF sampling trips 16 relationship between Kd(PAR) and TSS ............. 47
2.5. UF sampling trips 712 relationship between Kd(PAR) and TSS ............ 48
2.6. WQMN 19961998 relationship between Kd(PAR) and TSS ............... 49
2.7. WQMN 1999 relationship between Kd(PAR) and TSS. ................... 50
2.8. WQMN 19961998 relationship between turbidity and TSS. ............... 50
2.9. WQMN 1999 relationship between turbidity and TSS ..................... 51
2.10. HBOI year 1 relationship between Kd(PAR) and TSS. .................... 52
2.11. HBOI year 1 relationship between turbidity and TSS. ..................... 53
2.12. HBOI year 2 relationship between Kd(PAR) and TSS ..................... 53
2.13. HBOI year 2 relationship between turbidity and TSS. ..................... 54
5.1. Model results for all data sets using Ft. Pierce coefficients. ............... 109
5.2. Model results for all data sets using Marker 198 coefficients. ............. 109
5.3. Model results for SERC data set using Ft. Pierce coefficients. ............. 110
5.4. Model results for SERC data set using Marker 198 coefficients. ........... 110
5.5. Model results for UF synoptic trips 16 using Ft. Pierce coefficients......... 111
5.6. Model results for UF synoptic trips 16 using Marker 198 coefficients ....... 111
5.7. Model results for UF synoptic trips 712 using Ft. Pierce coefficients........ 112
5.8. Model results for UF synoptic trips 712 using Marker 198 coefficients. ..... 112
5.9. Model results for WQMN 1996 1998 using Ft. Pierce coefficients. ........ 113
5.10. Model results for WQMN 19961998 using Marker 198 coefficients. ....... 113
5.11. Model results for WQMN 1999 using Ft. Pierce coefficients ............. 114
5.12. Model results for WQMN 1999 using Marker 198 coefficients. ............. 114
5.13. Model results for HBOI Year 2 using Ft. Pierce coefficients .............. 115
5.14. Model results for HBOI Year 2 using Marker 198 coefficients. ............ 115
5.15. Model results for January March data using Ft. Pierce coefficients. ........ 118
5.16. Model results for April June data using Ft. Pierce coefficients ........... 118
5.17. Model results for July September data using Ft. Pierce coefficients. ....... 119
xvii
5.18. Model results for October December data using Ft. Pierce coefficients. .... 119
5.19. Model results for the south section of the IRL using Ft. Pierce coefficients. .. 121
5.20. Model results for the middle section of the IRL using Ft. Pierce
coefficients. .................................................. 122
5.21. Model results for the north section of the IRL using Ft. Pierce coefficients. .. 122
5.22. Model results for Banana River using Ft. Pierce coefficients .............. 123
5.23. Model results for Mosquito Lagoon using Ft. Pierce coefficients. .......... 123
5.24. Graph of Equation 4.10. Circles are the Ft. Pierce Inlet data, and squares
are the Marker 198 data. ......................................... 124
5.25. Model results for all data sets using SERC Monte Carlo coefficients. ....... 129
5.26. Model results for the SERC data set using SERC Monte Carlo
coefficients. .....................................................129
5.27. Model results for UF synoptic trips 16 using SERC Monte Carlo
coefficients. .............................................. .... 130
5.28. Model results for UF synoptic trips 712 using SERC Monte Carlo
coefficients. ................................................. 130
5.29. Model results for WQMN 19961998 using SERC Monte Carlo
coefficients. ..................................... ............ 131
5.30. Model results for WQMN 1999 using SERC Monte Carlo coefficients. ..... 131
5.31. Model results for HBOI Year 2 using SERC Monte Carlo coefficients. ...... 132
5.32. Model results for January March data using SERC Monte Carlo
coefficients. ................... ................................. 134
5.33. Model results for April June data using SERC Monte Carlo coefficients. ... 135
5.34. Model results for July September data using SERC Monte Carlo
coefficients ...................... .............................. 135
xviii
5.35. Model results for October December data using SERC Monte Carlo
coefficients. ................................................. 136
5.36. Model results for the south section of the IRL using SERC Monte Carlo
coefficients................................................. 138
5.37. Model results for the middle section of the IRL using SERC Monte Carlo
coefficients. ............................................ ........ 138
5.38. Model results for the north section of the IRL using SERC Monte Carlo
coefficients..................................................139
5.39. Model results for Banana River using SERC Monte Carlo coefficients....... 139
5.40. Model results for Mosquito Lagoon using SERC Monte Carlo coefficients. .. 140
5.41. Graph of Equation 4.10. Circles are the Ft. Pierce Inlet data, and
squares are the Marker 198 data. The solid line represents the curve
fitting the SERC "Monte Carlo" coefficients .................... . 141
5.42. Bottom sediment size (D50) from south to north in the IRL. ............... 142
6.1. Simulated TSS results used for calculating the light attenuation coefficient
for each i, j location in the grid including water quality and TSS loading. .... 149
6.2. Simulated Chlorophyll a results used for calculating the light attenuation
coefficient for each i, j location in the grid including loading of water
quality and TSS .................................................. 150
6.3. Interpolated color values with loading used for calculating the light
attenuation coefficient for each i, j location in the grid including. .......... 151
6.4. Depth of grid used to calculate the light attenuation coefficient, light at
the bottom of the grid, and percentage of incident light reaching the
bottom ... ................................................. 152
6.5. Simulated Kd(PAR) values throughout the IRL for a model run including
loading ........................................................ 153
6.6. Simulated amount of light reaching the bottom of the grid for the case
including loading. ....................................... ..... 154
6.7. Simulated percentage of incident light reaching the bottom of the grid
for the loading case. ............................................. 155
6.8. IRL segment locations............................................. 157
6.9. One year time series plot of simulated TSS concentrations for segments
14 for three loading cases. ....................................... 162
6.10. One year time series plot for simulated TSS concentrations for segments
58 for three loading cases. ....................................... 163
6.11. One year time series plots of simulated chlorophyll a concentrations for
segments 14 for three loading cases. ............................... 164
6.12. One year time series plots of simulated chlorophyll a concentrations for
segments 58 for three loading cases. .............................. 165
6.13. One year time series plots of interpolated color for segments 14 for
three loading cases. .................................... ....... 166
6.14. One year time series plots of interpolated color for segments 58 for
three loading cases. ............................................. 167
6.15. One year time series plots of simulated Kd(PAR) for segments 14 for
three loading cases. ............................................. 168
6.16. One year time series plots of Kd(PAR) for segments 58 for three
loading cases. ............................................... .. 169
6.17. One year time series plots of simulated light at bottom for segments
14 for three loading cases. ....................................... 170
6.18. One year time series plots of simulated light at bottom for segments
58 for three loading cases. ................... ..................... 171
6.19. One year time series plots of simulated percent of incident light at
bottom for segments 14 for three loading cases. ....................... 172
6.20. One year time series plots of simulated percent of incident light at
bottom for segments 14 for three loading cases. ....................... 173
A.1. Variation of predicted Kd(PAR) values with variations in chlorophyll a
concentration. ................................................. 182
A.2. Variations in predicted Kd(PAR) values due to variations in color. ......... 183
A.3. Variations in predicted Kd(PAR) due to variations in TSS concentration .... 183
A.4. Variations in predicted Kd(PAR) due to variations in TSS concentration .... 184
A.5. Variations in predicted Kd(PAR) due to variations in water depth .......... 184
A.6. Variations in predicted Kd(PAR) due to variations in time of day
between 1000 and 1400. ......................................... 185
A.7. Variations in predicted Kd(PAR) due to variations in time of day between 0800
and 1600. .......................................................185
A.8. Variations in predicted Kd(PAR) due to variations in day of the year. ....... 186
B.1. Monte Carlo results for the SERC data set. ........................... 188
B.2. Monte Carlo results for all data sets combined ......................... 189
C.1. Sites used for vertical grid cell tests. ............................. . 192
C.2. The amount of PAR calculated at each layer in the vertical grid at Site 1
using multiple Kd(PAR)s and one Kd(PAR) for the entire water column.
Taken at noon on each of the given days of a one year, 1998 model run. ...... 198
C.3. The amount of PAR calculated at each layer in the vertical grid at Site 2
using multiple Kd(PAR)s and one Kd(PAR) for the entire water column.
Taken at noon on each of the given days of a one year, 1998 model run. ...... 199
C.4. The amount of PAR calculated at each layer in the vertical grid at Site 3
using multiple Kd(PAR)s and one Kd(PAR) for the entire water column.
Taken at noon on each of the given days of a one year, 1998 model run. ...... 200
C.5. The amount of PAR calculated at each layer in the vertical grid at Site 4
using multiple Ka(PAR)s and one Kd(PAR) for the entire water column.
Taken at noon on each of the given days of a one year, 1998 model run. ...... 201
C.6. The amount of PAR calculated at each layer in the vertical grid at Site 5
using multiple Kd(PAR)s and one Kd(PAR) for the entire water column.
Taken at noon on each of the given days of a one year, 1998 model run. ...... 202
xxii
Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science
MODELING THE EFFECTS OF HYDRODYNAMICS,
SUSPENDED SEDIMENTS, AND WATER QUALITY ON LIGHT ATTENUATION
IN INDIAN RIVER LAGOON, FLORIDA
By
David Joseph Christian
December 2001
Chairperson: Dr. Y. Peter Sheng
Major Department: Civil and Coastal Engineering Department
Declining water quality due to anthropogenic effects has led to a decrease in seagrass
biomass in coastal waters throughout the world. Seagrass beds are vital components of the
coastal ecosystem providing both food and habitat to many species as well as acting as a
stabilizer for marine sediment. The seagrass beds in the Indian River Lagoon (IRL), a
shallow coastal lagoon along the East Coast of Florida, help to support a fishing industry
with a local impact of a billion dollars a year. A decline in light reaching the seagrass due
to poor water quality is suspected of being the major factor in seagrass loss in the IRL as well
as elsewhere.
In order to better evaluate water management decisions aimed at increased seagrass
growth in the IRL, the University of Florida has been developing an Indian River Lagoon
XX111
Pollutant Load Reduction Model (IRLPLR). This model integrates component models of
hydrodynamic, water quality, sediment, seagrass, and light attenuation processes. This thesis
focuses on the development of a light attenuation model and its integration into the IRLPLR
model. First five different sets of water quality and light data for the IRL are examined. The
report then evaluates regression, factorial, and numerical light attenuation models in order
to select the best light attenuation component for incorporation into the IRLPLR model.
Each model includes the known light attenuators: suspended solids, chlorophyll a in
phytoplankton, and color from dissolved organic matter. One, two, and three variable
regression models, as well as a three variable factorial model were developed for each of the
data sets, as well as each of the seasons of the year, and each of five sections of the IRL. The
numerical model was calibrated for each data set, season, and section to test the robustness
of the model and to see if incorporating spatial or temporal variations could improve model
results.
Variations in each of the regression and factorial models make it difficult to find a
single model, or a group of models, to best explain all of the data. One set of coefficients for
the numerical model was found that works well with each of the data sets, seasons, and
sections. The numerical model along with that set of coefficients was then incorporated into
the IRLPLR model.
xxiv
CHAPTER 1
INTRODUCTION AND BACKGROUND
1.1 Introduction and Background
The Indian River Lagoon (IRL), with more than two thousand identified species, is
one of the most diverse estuaries in the world (Barile et al., 1987). Lying on the East Coast
of Florida between Ponce de Leon Inlet in the north and Jupiter Inlet in the south, the IRL
stretches 341 km with an average depth of 1.2 m and a width varying between 0.4 and 12.1
km (Steward et al., 1994).
Seagrass beds play an important role in the IRL, as in estuaries in general. They are
highly productive and ecologically important habitats as well as important sediment
stabilizers (Zieman, 1982). Seagrass beds provide food for fishes and invertebrates as well
as protection from predators (Zieman, 1982). Because of these functions, the seagrass
meadows in south Florida's coastal areas are possibly the greatest nursery and feeding areas
in the region (Zieman, 1982). The importance of seagrass beds also influences water
management decisions. Because of their sensitivity to water quality conditions, as well as
their far reaching importance throughout the system, seagrass beds can act as a gauge for
short and long term water conditions (Vimstein and Morris, 1996).
While currently there are between approximately 70,000 and 90,000 acres of seagrass
beds in the IRL, this is a decrease from past years (Virnstein and Morris, 1996). Because of
2
their importance to sea life, the IRL seagrass beds are a foundation for the local fishing
industry, which generates about a billion dollars a year (Virnstein and Morris, 1996). This
works out to about $12,000/ year for each acre of seagrass coverage (Virnstein and Morris,
1996).
Seven species of seagrass are present in the IRL, giving it the highest diversity of
seagrass species of any estuary in North America (Dawes et al., 1995; Virnstein, 1995). The
seven species in order of decreasing abundance are:
Halodule wrightii shoal grass
Syringodium filiforme manatee grass
Halophila engelmannii star grass
Thalassia testudinum turtle grass
Halophila decipiens paddle grass
Halophilajohnsonii Johnson's seagrass
Ruppia maritima widgeon grass
Halophilajohnsonii occurs only in the southern portion of the IRL. The other six species are
the six species found in tropical and subtropical estuaries in the western hemisphere
(Virnstein and Morris, 1996). These seagrass species are seen in Figures 1.1 1.7. Figures
are from Florida Department of Environmental Protection (2001).
It is believed that the amount of photosynthetically active radiation (PAR), which is
the portion of light usable by plants, reaching the seagrass beds is the main factor controlling
the health of seagrass beds (Virnstein and Morris, 1996). Light attenuation in the water
column limits the amount of PAR which reaches the seagrass. The main light attenuators in
the water column are the water itself, dissolved yellow substance (color), phytoplankton, and
suspended particulates (Kirk, 1981). A decline in water quality, causing an increase in a light
attenuator, can lead to adverse effects on seagrass health.
Shoalgrass (Halodule wrightii)
Figure 1.1: Halodule wrightii
Manatcgrass
(Syrfnodifu fWfomrtw)
Figure 1.2: Syringodiumfiliforme
Figure 1.3: Halophila englemanii
urtluegrass
(Thaiass~a testudintom)
Figure 1.4: Thalassia testudinum
S 0lrqras&
)ohnhon'si Seagrass
(Halophifa johnson ii)
Paddlegrass
(Ha lophila decipiens)
Figure 1.5: Halophila johnsonii and Halophila decipiens
Figure 1.6: Ruppia maritima
6
The University of Florida, with funding from the St. Johns River Water Management
District (SJRWMD), is developing a pollutant load reduction model for the Indian River
Lagoon (IRLPLR) to help in making water management decisions (Sheng, 1999). The IRL
PLR model integrates hydrodynamic, water quality, sediment transport, light attenuation, and
seagrass models in order to predict changes in water quality and seagrass growth due to
changes in nutrient loading. For the reasons outlined above, light attenuation plays a major
role in the seagrass health, and therefore a robust light attenuation component of the model
is vital to the overall success of the IRLPLR model. The goal set forth by the SJRWMD is
to be able to consistently have seagrass growth out to a depth of 1.7 m (Virnstein and Morris,
1996). The light attenuation model is an important tool for finding where this is possible and
what water quality changes are needed in order to allow this to happen. This thesis examines
the available light and water quality data for the IRL along with regression, factorial, and
numerical models in order to select and incorporate a calibrated light attenuation model into
the overall IRLPLR model.
1.2 Light Definitions
Photon
To better understand what is being discussed here, a few definitions for light are
needed. Light is composed of electromagnetic energy packets called photons. The photons
contain properties of both a wave and a particle in what is known as a waveparticle duality.
Each photon carries a certain amount of radiant energy (Mobley, 1994). The amount of
energy q contained in a photon is related to the frequency of the wave V, and its
corresponding wavelength A by the speed of light c and Planck's
constant = 6.626 x 1034 J s:
he
q= hv= (1.1)
When we measure light, what the detector is actually measuring is the radiant energy
or the actual number of photons which are hitting it. Thermal detectors measure the heat
which comes from absorbing the photon's radiant energy. Quantum detectors measure the
number of photons which are hitting them. Quantum detectors were used in this study.
Often a diffuser will be placed in front of the detector so that only certain wavelengths will
be detected. In this case, a diffuser was used so that only wavelengths between 400 nm and
700 nm (the visible spectrum) would be measured.
Radiance
If a tube is put in front of the detector (Figure 1.7), such that the light being measured
is only allowed to enter the detector through a certain angle A Q2 the radiance L is being
measured. The equation which shows this measurement is:
SI; t; A) Q (J s' m2 srT1 nm1) (1.2)
L ; AtAAA AA
in which A Q is the amount of radiant energy the detector is exposed to, A t is the time
which the detector is exposed to the light, AA is the area of the diffuser that the light is
passing through to get to the detector, and A A is the wavelength interval which the diffuser
is allowing to pass through. L is shown as a function of. which the location of the
instrument in the water, t is time, E is the direction of the light, and 2 is the wavelength at
the center of the wavelength interval A .
Filter AX
Diffuser AA
Detector
Collecting Tube
Figure 1.7: The setup for a detector measuring radiance through an angle
AQ (Adapted from Mobley, 1994).
If everything on the left side of Equation 1.2 is taken to be infinitesimally small, then
the integral may be taken and Equation 1.2 becomes:
L ; t; A) d (W m2 sr' nm1) (1.3)
Radiance can be used to find the other needed radiometric values since it includes all
of the information needed about the light field, such as wavelength, spatial features, temporal
features, and directional features.
Since we want to know how much light is available to plants, it is important to know
how much light is coming down from all angles, not just the small angle A 2 To measure
this, the tube which was in front of the detector in Figure 1.7 is removed allowing light to
reach the diffuser from all angles above it and irradiance is measured.
Downward Radiance
Since this study is only concerned with the light which is coming from the sun, and
not that which is being reflected from the bottom of the estuary, the collectors are setup
facing the water surface in order to measure downward irradiance. The equation for
downward irradiance is then:
AQ
Ed (; t; ) A (W m2 nm1). (1.4)
AtAAAA
This is the same as the equation which explains radiance, except it now does not include the
angle A 2 since the light being measured is not being confined to just the one small angle.
Irradiance Sensors
There are two types of irradiance sensors. The first is a 2nI sensor as shown in
Figure 1.8. If this type of sensor is pointed upward, then it is measuring spectral downward
plane irradiance. If a beam of light is coming in incident to the sensor, and if the sensor is
of area AA, the entire area, AA, is being illuminated by the beam. If the beam is coming
in at angle 0, then the beam is only illuminating an area of AA cos 0. Since the collectors
are collecting photons from all of the angles between 7t and 27, they are integrating the
radiance L multiplied by Icos0I over all O's between T7 and 27t. For this study in which
sunlight is being considered, poU is used in place of 0. The downward plane irradiance being
measured is then related to the radiance as follows:
2 7r
Ed(x;t;,)= f fL(x;t;0; /;A/)\cos0ssin dW dO (1.5)
0=0o=2r
Diffuser
Filter
Detector
Figure 1.8: A 2n PAR sensor for measuring downward
irradiance (Adapted from Kornick, 1998).
The second type of irradiance sensor is the 4r7 sensor (Figure 19). Unlike the 2It
sensor, the 47 will collect photons from all angles equally. In order to just capture the
downward irradiance, a shield ( as seen in Figure 19) is needed to block any reflected light
coming up from below. Since all angles are being collected, the measurement is of
spectral downward scalar irradiance, Eod The relationship between this measurement and
the spectral radiance is shown in:
2g ~T/2
E ((;t;2Z) = 2 L(T; t;0; 0; A)sinWWd6
0=o9=o
(16)
Since the goal here is to find the light which is available for photosynthesis by
phytoplankton and seagrass, then the concern is with the photosynthetically active radiation
(PAR). Photosynthetically active radiation for phytoplankton includes both visible
Figure 1.9: A 47n PAR sensor for measuring downward irradiance.
wavelengths and near ultraviolet wavelengths. Since the near ultraviolet wavelengths are
quickly absorbed in the water column, PAR is usually estimated as just the visible
wavelengths between 400 nm and 700 nm (Mobley, 1994). This estimation is used in this
study.
Downward PAR and Light Attenuation Coefficient
The downwelling PAR reaching the bottom, or any depth in the water column, is
found using the Lambert Beer equation,
Iz = I*exp(Kd(PAR))*z) (17)
12
,where z is the depth below the water surface, Iz is the PAR at depth z, Io is the PAR just
below the water surface, and Kd(PAR) is the light attenuation coefficient for downward PAR
(Dennison et al., 1993). The LambertBeer equation follows a negative exponential due to
the nature of light attenuation in water. The wavelengths which are strongly absorbed
disappear quickly as the light enters the water. As the easily absorbed wavelengths
disappear, only the weakly absorbed wavelengths remain (Kirk, 1984). Therefore, if a light
attenuation coefficient is calculated in the upper portion of the water column it will tend to
be higher than if it is calculated, with the same water quality conditions, using a greater depth
(Kirk, 1984).
Kd(PAR) is calculated from PAR measurements in the data by using the rearranged
form of the LambertBeer equation,
K (PAR) = In (18)
This rearranged equation can be used to calculate Kd(PAR) using two measurements of PAR,
Iz and I, a distance of z depth apart. It can also use multiple points to calculate Kd(PAR) as
the slope of the best fit line resulting from the plot of 1I ) vs z where Io is the uppermost
PAR measurement and Iz is the PAR measurement at corresponding z depth below where Io
is measured.
13
In order to model the amount of PAR throughout the water column, Kd(PAR) is
modeled and then used in Beer's Law along with the PAR at the water's surface to calculate
PAR at the desired depths.
1.3 Seagrass and PAR Relationships
The minimum light requirements for submerged aquatic vegetation vary from 4 29%
of the light just below the water surface (Dennison et al., 1993). For comparison, land plants
in shaded areas require only 0.5 2% of the light just under the canopy (Hanson et al., 1987;
Osmond et al., 1983). Phytoplankton and benthic algae also require much lower light levels.
Green algae requires 0.05 1.0 % of incident light, while brown algae requires 0.7 1.5% of
incident light (Luning and Dring, 1979). Crustose red algae requires as little as 0.0005% of
incident light (Littler et al., 1985), while lacustrine and marine phytoplankton need 0.5 
1.0% of incident light (Parsons et al., 1979; Wetzel, 1975). The higher respiration
requirements of seagrasses have been pointed to as the reason for greater light requirements
for seagrasses than for phytoplankton (Dennison, 1987).
Light requirements vary between species. Halodule wrightti and Syringodium
filiforme have been found to each require 17.2% of incident light in Florida (Dennison et. al.
From personal communication with W. J. Kenworthy, 1993). Another report puts the light
requirement for S. filiforme in Florida at 18.3% of incident light (Duarte, 1991). Thalassia
testudinum in Florida has been found to require 15.3% of incident light (Duarte, 1991).
Kenworthy (1993) found much higher light requirements for H. wrightti and S. filiforme. His
results show a minimum of 27% of surface light needed in Jupiter Sound and 35% in Hobe
Sound. The Indian River Lagoon has a mild sloping bottom with a slope of about 2 cm m'
(Kenworthy, 1992). A gentle slope means that such a great range of light requirements could
14
mean a difference of many acres of seagrass. The same is true for changes in Kd(PAR)
(Kenworthy, 1993).
Dennison (1987) found that Zostera marina L. requires an average of 12.3 hours a
day of light above the light compensation point. The light compensation point is the light
level at which the oxygen the plant is getting from photosynthesis is equal to the amount of
oxygen it needs for respiration (Tomasko, 1993).
Duarte (1991) developed a relationship between compensation depth and the light
attenuation coefficient using data for thirty seagrass species and Ruppia. The equation he
developed is:
Z, = 1.86 / K (19)
in which Zc is the compensation depth and K is the light attenuation coefficient. This
equation compares well with similar equations. Dennison (1987) found a similar equation
for Zostera marina in the northeast United States. This is shown in Equation
110.
Zc = 1.62 / K (110)
Nielson et al. (1989) developed a similar equation for Z. marina in Danish estuaries as seen
in Equation 1.11.
Z, = 1.53/K (1.11)
Vicente and Rivera (1982) developed an equation for T. testudinum in Puerto Rican waters.
Their equation is Equation 1.12.
Z = 1.36 /K (1.12)
15
All of these relationships show the strong correlation between the depth at which seagrass
will grow and light attenuation.
More recently, Fong et al. (1997), Cerco et al. (2000), and Burd and Dunton (2001)
have developed seagrass models in which light is a major component in calculating seagrass
growth and death. Fong et al. and Cerco used light in conjunction with salinity, temperature,
and nutrients to model seagrass. Burd and Dunton had their model driven by the light
reaching the seagrass.
1.4 Previous Light Attenuation Models
McPherson and Miller (1994) modeled attenuation in Tampa Bay and Charlotte
Harbor by partitioning Kd(PAR) into portions due to water, color, chlorophyll a, and
nonchlorophyll suspended matter as in Equation 1.13:
k = kw + E2 *C2 + E3 C3 + E4 *C4 (1.13)
where k, is the light attenuation due to water; E2, E3, and E4 are the attenuation coefficients
for dissolved matter, chlorophyll a, and nonchlorophyll suspended matter, respectively; C2
is water color (PtCo units); C3 is chlorophyll a concentration (mg m3); and C4 is the
nonchlorophyll suspended matter concentration (mg m3).
McPherson and Miller (1987) also found the percent contribution of each component
to Kd(PAR) for Charlotte Harbor, Florida. Their findings include nonchlorophyll suspended
matter accounting for 72.5% of Kd(PAR), dissolved matter accounting for 21%, suspended
chlorophyll 4%, and water 3%. Phlips et al. (1995) found percent contributions in Florida
Bay. Their results show nonchlorophyll suspended matter accounting for 75% of Kd(PAR),
chlorophyll containing particles accounting for 14%, color accounting for 7%, and water
accounting for 4%.
16
Hogan (1983) used a model which took into account the Raleigh scattering of photons
by water molecules and Mie scattering from hydrosols as well as absorption. He found that
absorption dominates attenuation for most of the spectrum, except in the visible spectrum,
where scattering becomes most important between 350 nm and 500 nm. While the maximum
transmission of light occurs at 465 nm in clear water, the maximum transmission in turbid
waters occurs at about 550 nm. This is caused by suspended particulate matter absorbing and
scattering more of the shorter wavelengths. Because of this, total transmittance decreases
in turbid waters and the maximum transmittance occurs at the higher wavelengths (Hogan,
1983).
Kirk (1984) used Monte Carlo simulations in order to describe the apparent optical
property of the light attenuation coefficient using the inherent optical properties of absorption
and scattering. Through his Monte Carlo simulations, Kirk developed the equation:
Kd = + G(uo)aba] (1.14)
in which Kd is the vertical light attenuation coefficient for downwelling irradiance, po is the
cosine of the solar zenith angle, a, is the total absorption within the water, and b is the
scattering. G(,uo) is a function of /0 in which:
G() = g,9 g2 (1.15)
where g, and g2 are numerical constants which depend on the optical depth of interest. Kirk
(1984) calculated values for g, and g2 for depths in which the downward irradiance in the
17
water is reduced to 10% of its subsurface value (the midpoint of the photic zone), and for
where downward irradiance is 1% of its subsurface value. Kirk (1991) has found that
Equation 1.14 can be applied to most coastal water bodies studied by oceanographers.
Gallegos developed a physics based model for light attenuation (Gallegos and Correll,
1990; Gallegos, 1993; Gallegos and Kenworthy, 1996). His model uses Equations 1.14 and
1.15 developed by Kirk (1984). The model calculates Kd(PAR) in five nm increments
throughout the wavelength interval of interest. It can be used throughout the visible
spectrum to find the attenuation coefficient for PAR, or can be used for the
photosynthetically usable radiation (PUR) for a certain plant species. a, is found by summing
the absorption by color, chlorophyll a, water, and detritus. Absorption by water is read in
from a file for each wavelength of interest. Absorption due to the other components are
calculated from equations. Scattering, b, is calculated for turbidity. a, and b are then used
to calculate Kd() for each 2 used. Kd), along with incident light at that wavelength are
then used to calculate the light at the depth of interest using the LambertBeer equation at
that wavelength. The incident light and light at depth are each integrated over the wavelength
interval of interest and used in a rearranged form of the LambertBeer equation to calculate
Kd(PAR) over the wavelength interval. Tests by Gallegos have shown this model to work
as well as Kirk's (Gallegos, 2001).
Gallegos has calibrated and used his model in the Rhode River and Chesapeake Bay
(Gallegos and Correll, 1990). He then calibrated and used the model near Ft. Pierce, FL in
the IRL (Gallegos, 1993; Gallegos and Kenworthy, 1996). The results show a coefficient of
variation of around 15%. He notes, and it is important to remember here as well, that the
18
observed Kd(PAR) values also contain error which contributes to the variation between
modeled and observed values.
There are a few advantages to Gallegos's model. The first is that it is based on
physics with coefficients that can be calibrated to the area of interest. There are only four
coefficients which need to be considered. Three are used to determine the absorption by
detritus, while the fourth is used to calculate absorption by color. The next advantage is that
the use of the LambertBeer equation enables depth to be included in the calculation. The
model used by McPherson and Miller does not allow for this. Another advantage to
Gallegos's model is that it can easily be adapted to calculate the attenuation coefficient for
PUR as opposed to PAR for use with a specific plant species.
1.5 This Study
Two approaches have been taken here to finding the best model for Kd(PAR) given
the current data sets. The first approach has been to develop a numerical model based on the
work of Gallegos (1993) in the Indian River Lagoon. The second approach has been to
develop a stepwise regression model using the PROC REG procedure in SAS software. For
both of these approaches, total suspended solids, chlorophyll a (chl_a), and color were used
in the prediction of Kd(PAR).
Chapter 2 describes the data sets used in this thesis. It also gives the statistics on the
data sets used. Chapter 3 shows the regression models developed for the different data sets,
segments of the IRL, and different seasons of the year. Chapter 4 outlines the numerical
model used including the equations and background. Chapter 5 takes that one step further
and describes the stand alone light attenuation model used for testing. This also includes
calibration which was done for the model and results of test runs. Chapter 6 explains the
19
coupling of the light attenuation model to the rest of the IRLPLR model. It includes results
of runs for 1998 with regular loading of nutrients and zero loading of nutrients. Chapter 7
includes discussion and conclusions for this thesis.
CHAPTER 2
DATA SETS
2.1 Introduction
Data sets from five sources are used in calibration and verification of the IRLPLR
light attenuation model. All five data sets include both light data as well as water quality
data. The five data sets include data taken by Gallegos of the Smithsonian Environmental
Research Center (SERC) for calibration of his numerical model (Gallegos, 1993), data
collected by UF during twelve synoptic sampling trips in 19971998, Water Quality
Monitoring Network Data (WQMN) received from SJRWMD, and data collected by Hanisak
at Harbor Branch Oceanographic Institute (HBOI). Data collected Phlips (2000) for the IRL
PLR project are also used.
2.2 Sampling Procedures
The following section outlines the sample sites for each of the data sets. When
available, equipment used for sampling are also shown. Data from the different groups cover
1994 1999.
2.2.1 SERC Data Set
Gallegos (1993) sampled light and water quality concurrently near Ft. Pierce Inlet
for calibration of a light attenuation model for the southern part of the IRL. No set frequency
was used for the sampling, but sampling occurred over several days in December, 1992; and
March and April of 1993.
21
Light sampling was done measuring downwelling PAR using 27t Licor 192B
underwater quantum sensors. Sampling was done over the visible spectrum, with the
spectrum being divided into 5 nm increments by interference filters. A deck cell on board
the boat was used to normalize each channel of the spectral radiometer (Gallegos, 1993a).
Vertically integrated water samples were used for the water quality. They were sampled
using a 2 liter Labline Teflon bottle. For sampling, the bottle was slowly lowered, and then
brought back up more rapidly than it could fill. An initial sample was used for rinsing in
the field. Once rinsed, multiple samples were taken each day at each station. The laboratory
methods used were submitted to the FDEP in a Research Quality Assurance Plan by Gallegos
(1993a). The locations for SERC sampling are shown in Table 2.1, while the water quality
sampling relevant to the light attenuation model is shown in Table 2.2.
Table 2.1: Sample sites used in the SERC study.
Site Latitude N Longitude W Northing UTM Easting UTM
(m) (m)
Ft. Pierce Inlet 270 28'06.0" 800 19' 51.0" 3038522 566137
Taylor Creek,
Near Channel
Marker 184
Near Channel 270 22' 16.8" 800 16'38.4" 3027807 571486
Marker 198
Near an Inlet 270 28'03.6" 800 18'58.8" 3038456 567570
Range Marker
Taylor Creek Furthest location upstream that could be reached. Designated
Upstream C25 C25 since Taylor Creek receives flow from canal structure C25.
Channel Marker Near the entrance to Harbor Branch Oceanographic Institute.
172
Near Marker 186 Near Ft. Pierce Inlet in turning basin.
Table 2.2: SERC water quality variables used in the light attenuation model.
Variable Collection Method Units Symbol
Color Niskin Bottle Pt Units color
Total Suspended Solids Niskin Bottle mg/L TSS
Turbidity Niskin Bottle NTU turb
Chlorophyll a Niskin Bottle pLg/L chl_a
2.2.2 UF Data Set
UF conducted twelve synoptic sampling trips between April, 1997 and May, 1998
(Sheng and Melanson, 1999). The first six trips were done at a frequency of twice a month.
The second six were done at a frequency of about once a month. In the first six sampling
trips, fortyfive sites were sampled during each trip. Thirty sites were sampled during each
of the second six trips. Sampling included light measurements using three 4t submersible
Licor sensors with the data stored in Licor dataloggers. It also included in situ water quality
sampling using Hydrolab datasondes as well as bottle samples which are analyzed in the
laboratory. Laboratory bottle samples were collected using a modified Niskin bottle (Sheng
and Melanson, 1999) And transported within 24 hours to the laboratory for analysis.
Light data and water quality sampling were always done at the same time. Vertical
positions of the water quality sampling were consistently at 20% and 80% of the total depth,
while those for the light measurements varied between sampling trips. For the first trip,
measurements were taken simultaneously just below the surface and at 20% of total depth,
then simultaneously at just below the surface and 50% of total depth, and then
simultaneously at just below the surface and at 80% of total depth. Three replicates of each
were taken about a minute apart. For trips two through five, all three Licor sensors were
23
deployed at once. One at 20% of total depth, one at 50% of total depth, and one at 80% of
total depth. Again, at least three replicates were taken when possible. For the final seven
trips, light measurements were taken simultaneously atjust below the surface, at 50% of total
depth, and at 80% of total depth. Once again, three replicates were done with a minute
between each, when possible.
Table 2.3 shows the sampling date for each and every UF sampling trip. Table 2.4
contains the sampling information for relevant light attenuation model variables. Table 2.5
Table 2.3: UF synoptic sampling trips were carried out on these dates.
Trip Number Date of Trip Julian Date
1 April 8, 1997 98
2 April 25, 1997 115
3 May 6, 1997 126
4 May 20, 1997 140
5 June 9, 1997 160
6 June 25, 1997 176
7 November 20, 1997 324
8 January 29, 1998 29
9 February 26, 1998 57
10 March 26, 1998 85
11 April 30, 1998 120
12 May 28, 1998 148
Table 2.4: UF water quality variables used in the light attenuation model.
Variable Collection Method Units Symbol
Color Niskin Bottle Pt Units color
Total Suspended Solids Niskin Bottle mg/L TSS
Chlorophyll a Niskin Bottle mg/m3 chl_a
Table 2.5: Sample sites used during UF synoptic sampling trips.
Site Number Site Number Latitude N Longitude W Northing UTM (m) Easting UTM (m)
Trips712 Trips 16
1 1 270 55' 54" 80o 31'21" 3089768 546981
2 3 27058' 51" 80032' 12" 3095209 545566
3 6 280 02' 48" 80034' 27" 3102488 541852
4 9 28007' 27" 80036'33" 3111062 538385
5 11 28010'21" 80038'12" 3116408 535668
6 14 28014' 21" 80040'03" 3123785 532621
7 15 280 15'45" 80040'42" 3126367 531551
8 13 28012' 51" 80039'21" 3121037 533773
9 8 28006'00" 800 35'54" 3108388 539458
10 2 27057'27" 80031'36" 3092628 546560
11 16 28017' 09" 80o41'27" 3128949 530318
12 19 28021'39" 80o43'22" 3137250 527161
13 22 28026'21" 80044'51" 3145923 524709
14 24 28029'06" 80045'48" 3150997 523165
15 28 28032'36" 80 46' 18" 3157458 522337
16 31 28034'30" 80o45'39" 3160876 523390
17 30 28034' 12" 80o46'54" 3160411 521354
18 29 28032'51" 80o44'30" 3157926 525271
19 21 28024'43" 80044'26" 3142915 525402
20 17 280 18' 25" 80042'00" 3131310 529414
21 42 28045' 21" 80049'33" 3180992 517004
22 44 28044'03" 80047'33" 3178597 520262
23 40 28043' 18" 80048'51" 3177208 518149
24 39 28041'57" 80047' 15" 3174720 520758
25 37 28040'09" 80048'36" 3171392 518565
26 35 28037' 24" 80048' 00" 3166316 519551
27 33 280 35' 48" 80047'57" 3163362 519637
28 36 28038' 39" 80 48'27" 3168624 518814
29 38 28041' 09" 80o48'48" 3173239 518237
30 45 28043' 37" 80045'49" 3180992 517004
Table 2.6: Additional sampling sites used during UF sampling trips 16
Site Number Latitude N Longitude W Northing UTM (m) Easting UTM (m)
4 280 00' 18" 800 32' 45" 3097883 544655
5 280 01' 24" 800 33' 36" 3099909 543255
7 280 04' 30" 800 35' 09" 3105624 540696
10 280 08' 51" 800 37'21" 3113643 537068
12 280 11' 39" 800 38' 36" 3118807 535007
18 280 19' 57" 800 42' 36" 3134133 528427
20 280 23' 21" 800 43' 54" 3140387 526273
23 280 27' 48" 800 45' 06" 3148600 524313
25 280 29' 21" 800 44' 39" 3151463 525041
26 28030' 45" 80046' 24" 3154043 522181
27 280 31' 00" 800 45' 36" 3154507 523485
2.2.3 WOMN Data
Data was also obtained from the Water Quality Monitoring Network (WQMN). The
WQMN, coordinated by SJRWMD, involved sampling monthly at thirtyfour sites
throughout the lagoon. Each sampling run collects between two and six samples at each
location over a three day period. Care is taken in the light modeling to use light and water
quality data which were taken at the same time on the same day at the same site.
Data used for this analysis were taken between March 1996 and May 1999. For
reasons discussed later, these data are split into two data sets. The first data set includes
1996 1998, while the second data set contains data collected in 1999. The locations for the
WQMN sample sites are shown in Table 2.7
2.2.4 HBOI Data
Hanisak at Harbor Branch Oceanographic Institute sampled at seven sites throughout
the IRL between 1994 and 1995. PAR measurements were made every 15 minutes using
both 2xt and 4t Licor sensors. The sensors were deployed at the top and middle of the
seagrass canopies at the sampling sites. Water quality measurements were made weekly.
Care was taken to use only corresponding light and water quality measurements for model
calibration. A detailed account of HBOI sampling procedures is available in their Florida
Department of Environmental Protection (FDEP) Quality Assurance and Quality Control
Table 2.7: Sites sampled during WQMN sampling trips.
Sample Latitude N Longitude W Northing UTM (m) Easting UTM (m)
Site
B02 28026'01" 80038'22" 3145321 535330
B04 28022'00" 80038'00" 3137907 535951
B06 28017'00" 80038'00" 3128675 535979
B09 28011'56" 80037'32" 3119323 536771
CCU 28004'39" 80036'08" 3105884 539105
EGU 280 07'25" 800 37'50" 3110983 536305
GUS 27028'05" 80032'41" 3093780 544800
HUS 28009'55" 80038'31" 3115595 535173
102 28044'20" 80048'02" 3179103 519496
107 28036'12" 80047'54" 3164086 519739
110 280 30'04" 80046'08" 3152768 522639
113 28023'34" 80044'10" 3140773 525873
116 280 16'40" 80040'36" 3128048 531731
118 28011'40" 80038'56" 3118824 534482
121 28007'30" 80037'00" 3111141 537669
123 280 04'12" 80035'40" 3105056 539871
127 27056'44" 80031'46" 3091293 546312
IRJ01 27047'48" 80026'56" 3074834 554311
IRJ04 27041'33" 800 23' 14" 3063324 560443
IRJ05 27039'28" 800 22'32" 3059484 561613
IRJ07 27037'11" 80022'04" 3055272 562401
IRJ10 27041'57" 80023'39" 3064059 559754
IRJ12 27036'34" 80022'01" 3054134 562489
ML02 28043'35" 80043'05" 3177735 527556
SUS 27051'15" 80029'29" 3081185 550098
TBC 28049'14" 80051'41" 3188142 513546
TUS 28001'58" 80034'48" 3100937 541305
V05 29000'29" 80054'34" 3208910 508841
V11 28057'09" 80050'41" 3202762 515153
V17 28052'41" 80050'22" 3194515 515678
VMC 27038'57" 80024'08" 3058517 558987
VSC 270 36'17" 800 22'58" 3053603 560930
27
(QAQC) manual. The HBOI sample information is shown in Table 2.8 and the sample sites
are shown in Table 2.9.
Table 2.8: HBOI water quality variables used in the light attenuation model.
Variable Collection Method Units Symbol
Color Niskin Bottle Pt Units color
Total Suspended Solids Niskin Bottle mg/L TSS
Turbidity Niskin Bottle NTU turb
Chlorophyll a Niskin Bottle pg/L chl_a
Table 2.9: Sample sites used during the HBOI study.
Site Name Site Latitude N Longitude W Easting Northing
Symbol UTM (m) UTM (m)
Banana BR 280 30' 21" 800 35'20" 540242 3153359
River
Melbourne MB 290 09' 01" 80038' 07" 535489 3224728
Turkey TC 28001'52" 800 34'35" 541655 3082043
Creek
Sebastian SN 270 51' 42" 800 29' 31" 550036 3082043
North
Sebastian SS 270 51' 00" 800 29' 18" 550392 3080734
South
Vero Beach VB 270 34' 51" 800 21' 50" 562791 3050990
Link Port LP 270 32' 10" 800 21'00" 564182 3046047
2.2.5 Phlips Data
Phlips sampled twentyfour sites throughout the lagoon during three sampling trips
in July, October, and November of 1999. Light sampling was done using a Licor PAR
quantum sensor. Only data collected during the October trip are used in this analysis since
only samples taken during this trip included TSS for use in the light attenuation model.
2.3 Data Set Statistics
The following are the statistics for each of the data sets used in this study. The
maximum and minimum values as well as means and standard deviations are given for the
model attributes of each data set.
2.3.1 SERC Data Set
Table 2.10 shows the statistics for Gallegos's SERC data set. This is the data set
used by Gallegos for calibration of his light attenuation model in the southern partof the IRL.
The higher color numbers are associated with the outflow from Taylor Creek, which contains
outflow from Canal Structure 25. The color in this area was sometimes seen as a lens of
color in the upper half meter of the water column (Gallegos, 1993).
Table 2.10: Data set statistics for the data collected during the SERC study.
Variable Minimum Maximum Mean Standard
Deviation
Turbidity (NTU) 1.40 6.40 3.00 1.18
TSS (mg/L) < 5.00 28.60 10.71 4.94
Chlorophyll a (gg/L) 1.11 30.77 6.18 6.27
Color (Pt Units) < 7.00 94.00 26.34 25.59
Kd(PAR) (m1) 0.55 2.47 1.27 0.46
2.3.2 UF Data Sets
The UF data are divided into two data sets. The first includes data collected during
synoptic sampling trips 16, while the second includes data collected during synoptic
sampling trips 712. This division of data sets is for a few reasons. The first six synoptic
trips took place over a three month span in the spring of 1997. The second six synoptic
tripstook place over a seven month span beginning in November, 1997. As explained earlier,
the light sampling techniques varied during the first six trips, but were all uniform during the
second six. One lab was used for sample analysis during the first six sampling trips, but a
different lab was used during the second six trips. For these reasons, it is logical to divide
all of the UF data into these two data sets. The statistics for each of these data sets are given
in Tables 2.11 and 2.12.
Table 2.11: Statistics for the data collected during UF synoptic sampling
trips 16.
Variable Minimum Maximum Mean Standard
Deviation
TSS (mg/L) < 5.00 55.00 7.88 6.50
Chlorophyll a ([lg/L) < 1.00 20.30 5.26 2.84
Color (Pt Units) < 7.00 26.00 14.72 3.21
Kd(PAR) (m1) 0.05 4.62 1.02 0.64
The greatest differences between these two data sets are in TSS and color values. In
both instances, the data from trips seven through twelve have higher maximums and means.
The interesting point to be made here is that even though both the color and the TSS mean
30
values are higher during the second six trips, the mean Kd(PAR) value is about the same.
This will be discussed more later.
Table 2.12: Statistics for the data collected during UF synoptic sampling trips 712
without transformed TSS.
Variable Minimum Maximum Mean Standard
Deviation
TSS (mg/L) 9.24 120.50 30.58 16.34
Chlorophyll a (tg/L) 1.38 31.80 7.22 4.81
Color (Pt Units) 10.00 90.00 22.46 14.00
Kd(PAR) (m1) 0.33 2.97 0.97 0.45
2.3.3 WOMN Data Set
As described earlier, this study uses data collected by the Water Quality Monitoring
Network between 1996 and 1999. This data set has been broken into two separate data sets
for the purpose of analyzing the data for the light attenuation model. The first data set
contains data from 19961998. The second contains data from 1999. This split is done to
try and account for much higher TSS values found in the 1999 data.
Tables 2.13 and 2.14 show the large difference between the mean TSS values in the
two data sets. The means for both chlorophyll a and color are comparable. The mean value
for Kd(PAR) during 1999 is only slightly higher than that for 19961998, although the mean
TSS is much higher. The mean values of turbidity are comparable. HigherTSS value should
lead to higher turbidity values if the sampling is being done at the same locations with the
same sediment types. This issue of high TSS will also be addressed later.
Table 2.13: Data set statistics for data collected by WQMN from March 1996 through
1998.
Variable Minimum Maximum Mean Standard
Deviation
Turbidity (NTU) < 1.00 77.40 5.23 5.25
TSS (mg/L) < 5.00 157.33 13.28 14.02
Chlorophyll a (pg/L) < 1.00 49.68 7.58 6.49
Color (Pt Units) <7.00 85.00 24.23 12.12
Kd(PAR) (m1) 0.24 3.99 1.07 0.53
Table 2.14: Data set statistics for data collected by WQMN between March and May
1999 without transformed TSS.
Variable Minimum Maximum Mean Standard
Deviation
Turbidity (NTU) < 1.00 43.00 7.74 5.10
TSS (mg/L) 13.60 135.00 62.96 26.46
Chlorophyll a (pg/L) 1.34 14.87 5.88 3.04
Color (Pt Units) 10.00 52.00 21.83 8.40
Kd(PAR) (m1) 0.43 2.49 1.28 0.55
2.3.4 HBOI Data Sets
The Harbor Branch data is split into two data sets for a couple of reasons. The first
is that when we received the data, we received one year at one time and then the second year
at another time. Since both years had a large amount of data, it was decided to keep them
separate. The other reason is that the time of day when the light sample was taken is an
important input for the numerical light attenuation model. Time of day was not received
32
for the first year's data. Because of this, the first year's data are not able to be used in the
numerical model. By keeping the two year's data separate, the second year's data are able
to be used in the numerical model and thus for comparison with the regression model results
and with numerical model results of other data sets. The first year's data are still used for
the regression model. The statistics for the two years of HBOI data are shown in Tables 2.15
and 2.16.
Table 2.15: Data set statistics for HBOI data collected during HBOI's first sampling year
without transformed TSS.
Variable Minimum Maximum Mean Standard
Deviation
TSS (mg/L) < 5.00 199.99 57.00 26.86
Chlorophyll a (pg/L) < 1.00 96.22 13.15 12.67
Color (Pt Units) <7.00 128.20 17.63 18.82
Kd(PAR) (m') 0.04 6.88 1.67 1.31
Table 2.16: Data set statistics for HBOI data collected during HBOI's second sampling
year without transformed TSS.
Variable Minimum Maximum Mean Standard
Deviation
TSS (mg/L) 24.01 159.30 67.42 24.02
Chlorophyll a (ig/L) 3.29 79.09 16.54 12.04
Color (Pt Units) <7.00 165.60 19.31 19.66
Kd(PAR) (imn) 0.09 6.59 1.76 1.07
Notice that for each year of sampling by Harbor Branch, the mean values for each of
the variables are similar. Other than for WQMN 1999, the mean TSS values for both years
33
are higher than for the other data sets shown so far. The mean Kd(PAR) values for each year
are also much higher than they are for the other data sets, including WQMN 1999.
2.3.5 Phlips Data Set
The Phlips data set is by far the smallest of the data sets used with only nineteen data
records. This is because only one day of sampling included TSS sampling. The statistics for
this data are shown in Table 2.17.
Table 2.17: Data set statistics for data collected by Phlips during their October 1999
sampling trip in which TSS data were collected.
Variable Minimum Maximum Mean o
TSS (mg/L) 5.40 24.50 14.72 5.59
Chlorophyll a (pg/L) 8.50 28.00 18.49 5.05
Color (Pt Units) 14.00 28.00 20.05 4.21
Kd(PAR) (m') 0.77 3.63 1.57 0.64
2.3.6 All Data Sets Comparison
The previous section shows that there are great differences between the mean values
of the variables in different data sets. Not only do the mean values of a variable vary
between data sets taken by different groups, but they also vary between data sets taken bythe
same group. Table 2.18 shows the mean values for each variable in each data set for easy
comparison.
UF Trips 712 have mean Kd(PAR) values which are in line with the other data sets,
with UF Trips 712 having the lowest mean Kd(PAR) value of all of the data sets. As for the
mean color values, UF Trips 16 has the lowest mean value of 14.72 Pt. Units, while SERC
Table 2.18: Mean values of variables of interest from each of the data sets used in this
study without transformed TSS data.
Data Set Chlorophyll a Color TSS Kd(PAR)
(__g/L) (Pt Units) (mg/L) (m1)
SERC 6.18 26.34 10.71 1.27
HBOI 1994 13.15 17.63 57.00 1.67
HBOI 1995 16.54 19.31 67.42 1.76
UF Trips 16 5.26 14.72 7.88 1.02
UF Trips 712 7.22 22.46 30.58 0.97
WQMN 7.58 24.23 13.28 1.07
19961998
WQMN 1999 5.88 21.83 62.96 1.28
Phlips 18.49 20.05 14.72 1.57
has the highest mean value of 26.34 Pt. Units. All of the mean values for the other data sets
fall within this relatively narrow range. The chlorophyll a data also fall within a relatively
narrow range between 5.26 pg/L for UF Trips 16 and 18.49 Vlg/L for the Phlips data set.
Since we are trying to find relationships that can be used to create a model for
Kd(PAR), some of these mean values do not make sense, such as all of the mean values for
UF Trips 16 being lower than the mean values for UF Trips 712, except for Kd(PAR). With
this being the case, we need to try to analyze the data sets more to see if these trends are seen
not only for the whole data set, but also for individual samples.
2.4 The Relative Importance of Various Factors for Light Attenuation
As stated earlier, this modeling effort concentrated on predicting K/PAR) using the
important, measurable, water quality parameters of TSS, color, and chlorophyll a
35
concentration. Since the mean values for each of these variables vary between the different
data sets, an analysis was done in order to find the relative contributions of these variables
to the KdPAR).
2.4.1 Equations Used to Calculate K/PAR) Attributable to Each Variable
Using an analysis employed by McPherson and Miller (1994) in Tampa Bay and
Charlotte Harbor, Florida, and by Phlips et al. (1995) in Florida Bay, the contributions to
K/PAR) are found for chlorophyll a, color, nonchlorophyll suspended solids (tripton), and
water. This is shown in Equation 2.1:
Kd( PAR) = Kw + Kchla Kco + Ktrip (2.1)
where K, is the contribution to K/PAR) due to water, Kchl is the contribution due to
chlorophyll a, Kcol is the contribution due to color, and Ktrip is the contribution due to tripton.
K, is taken to be 0.0384 m1 (Lorenzen, 1972), Kchla is calculated by multiplying the
chlorophyll a concentration by 0.016 m2 g1 (Phlips, personal communication), and Kco, is
calculated by multiplying color by 0.014 pt~' m' (McPherson and Miller, 1987). There is not
a coefficient for use in finding Krip, therefore it is found by subtracting the other KdPAR)
components from the measured KdPAR) as in Equation 2.2.
Ktrip = Kd(PAR) K K cla Kc (2.2)
Because Krip must be backed out for this analysis, this is not a method that can be used to
model KdPAR). Also note that tripton is used in this analysis, but it is not included in any
of the data sets. The TSS values included in the data sets include tripton as well as
36
chlorophyll suspended solids. Tripton can be calculated by subtracting chlorophyll a
concentrations corrected for pheophytin from TSS concentrations. Since TSS concentrations
are usually much higher than chlorophyll a concentrations1, tripton concentrations are close
to that of TSS.
Equation 2.1 is able to be used since the attenuation coefficient can be partitioned
into partial attenuation coefficients corresponding to different components of the water body
(Kirk, 1983). Kirk did warn, though, and it should be noted that the nature of each of the
attenuation coefficient contributions can be different between the components. Also, he
warned that KdPAR), and thus the contributions to it by each component are not linear (Kirk,
1983).
2.4.2 Data Set Analysis
After values were found for Khl,,, Kcot, and Krip, each value was divided by KdPAR)
and then multiplied by one hundred in order to find the percent contribution to KdPAR).
Table 2.19 shows the average percentages of KdPAR) due to each component for each data
set.
Except for WQMN 19961998 and UF trips 712, the other data sets all have tripton
accounting for more than 60% of the light attenuation coefficient. Chlorophyll a accounts
for between 7.80% of KdPAR)for the SERC data set and 16.35% of KdPAR) for the HBOI
Year 2 data set. Color is responsible for between 17.02% of KdPAR) for the HBOI Year 2
data set and 33.63% of KdPAR) for the WQMN 19961998 data set.
1 See Table 2.18, remember that TSS has units of mg/L and Chlorophyll a has units of pg/L.
Table 2.19: Percent of Kd(PAR) due to each attenuator in this study.
Data Set Average %Kd(PAR) Average % Kd(PAR) Average % Kd(PAR)
Due to Color Due to Chlorophyll a Due to Tripton
WQMN 33.63 11.27 50.84
19961998
WQMN 1999 26.22 8.00 62.17
UF Trips 16 25.62 9.56 60.10
UF Trips 712 32.84 12.69 49.94
HBOI Year 2 17.02 16.35 63.68
SERC 25.07 7.80 63.74
All Sets 24.04 13.03 59.14
Therefore, for each of the data sets, tripton contributes the most to light attenuation. The
Phlips data set was not used because it is too small.
2.4.3 Percentage of Each Measured K/PAR) Due to Each Variable
Figures 2.1 through 2.3 show how the percent of the light attenuation coefficient due
to color, chlorophyll a, and tripton, respectively, varies over the range of measured K/PAR)
values. Each point on the graph represents the percentage for data measured along with the
KdPAR) value. Notice that color and chlorophyll a both contribute a greater percentage to
the light attenuation coefficient at lower measured values of K/PAR) than they do at higher
measured values of K/PAR), where tripton clearly contributes a higher percentage.
Because of this discrepancy between different K(PAR) values, further analysis was
done to see what the relative contribution of each component is to the higher and lower
measured KdPAR) values. The average values for the percentage of K(PAR) due
100 
0
W 90
90
0 80 0
0 70 x
*1) 6 0  L D  0 
0 0
S60 8 o
S50 0
0" 40 j ^ a n o
S30 4 x
2 30 C o 0
20 %o o 
0 00
o 0 so o 0 I o0
0 a
0 1 2 3 4 5
Kd(PAR) (m1)
Figure 2.1: Percentage of Kd(PAR) due to chlorophyll a.
120
a xx x x
O
100 a
O 1o
Sx
Y x x
80 x 2
0 0
20 0 x 0 0 0
2 3 4 5
Observed Kd(PAR) (m1)
Figure 2.2: Percentage of Kd(PAR) due to color.
20
Figure 2.2: Percentage of Kd(PAR) due to color.
6 7
6 7
120
=WQMN 19961998
C100 o WQMN1999
40 HBOI Year 2
Soo
02 ^  .I 4 I5 I ;
0 0
0I 60. .,, ^, xUF712
S40:
80
SKd(PAR) (m1)
Figure 2.3: Percentage of Kd(PAR) due to tripton.
to color, chlorophyll a, and tripton for each data set above and below K/PAR) equal to 1.00
m', as well as above and below the average K/PAR) for each data set are shown in Tables
2.20 and 2.21.
KdPAR) equal to 1.00 m' is chosen as a cutoff here because examination of Figures
2.1 and 2.2 show curves in the plots around this point. Another reason is because this is
about the point where, in some cases, the numerical model (described in Chapters 4 and 5)
goes from over predicting K/PAR) to under predicting K/PAR). The mean K(PAR) value
for each data set is chosen as a cutoff in order to see if there is a difference in data for the
upper and lower K/PAR) values of the data set. Tables 2.20 and 2.21 show that for higher
KdPAR) values, the average percentage of K/PAR) due to tripton is higher than for the lower
KdPAR) values. The exception is the SERC data set. This is because of the high color
values during some of the SERC sampling. For color and chlorophyll a, the average
Table 2.20: Percentage of K/PAR) due to color, chlorophyll a, and tripton for each data set for K(PAR) values above and below
1.00 m1.
Data Set % K/PAR) Due to Color % K/PAR) Due to Chl_a % K(PAR) Due to Tripton
Kd/PAR) < 1 KjPAR) > 1 KdPAR) < 1 K(PAR) > 1 K/PAR) 1 KdPAR) > 1
WQMN 19961998 38.11 28.18 11.54 10.95 44.89 58.09
WQMN 1999 35.82 20.01 9.54 7.00 49.41 70.42
UF Trips 16 30.14 14.65 10.79 7.12 53.50 75.40
UF Trips 712 33.67 30.97 13.98 9.74 47.05 56.50
HBOI Year 1 20.30 14.12 17.57 12.43 55.99 71.33
HBOI Year2 24.35 15.37 22.00 15.08 47.18 67.41
SERC 14.35 31.06 6.47 8.54 74.57 57.68
All Sets 30.76 19.00 13.67 12.56 49.92 66.06
Table 2.21: Percentage of KdPAR) due to color, chlorophyll a, and tripton for each data set for K/PAR) values above and below the
mean KdPAR) value for each data set.
Data Set Mean Avg % K/PAR) Due to Color Avg % K/PAR) Due to Chl_a Avg % K/PAR) Due to
KdPAR) Tripton
K/PAR) KdPAR) K(PAR) K(PAR) KdPAR) K/PAR)
< Mean > Mean < Mean > Mean < Mean > Mean
WQMN 1.07 37.61 27.59 11.59 10.79 45.50 58.97
19961998
WQMN 1.28 32.50 16.53 10.08 4.78 52.84 76.58
1999
UF 16 1.02 30.06 14.40 10.77 7.06 53.63 75.75
UF 712 0.97 33.80 30.90 14.18 9.63 46.68 56.61
HBOI
HB1 1.67 17.84 13.70 15.89 11.35 61.53 73.54
Year 1
HBOI
HBa 1.76 18.63 14.86 18.47 13.51 58.92 70.08
Year 2
SERC 1.27 17.93 35.14 6.71 9.33 71.22 53.18
All Sets 1.31 28.64 17.05 13.43 12.44 52.95 68.54
42
percentage of KdPAR) due to each of those is generally higher for the low KdPAR) values
than for the higher K(PAR) values. Of course, the exception again is the SERC data set. A
portion of the SERC data set was collected near Taylor Creek, which contains outflow from
a canal structure. Data from the Taylor Creek area show higher color data including an
occasional lens with high color values on the surface of the water.
In previous studies using this analysis, tripton also accounted for the largest relative
percentage of K/PAR), but color and chlorophyll a varied. Phlips et al. (1995) studied
seventeen sites sampled during 1993 and 1994 in Florida Bay, Florida. The average
percentages for all of the sites together show tripton accounted for approximately 74.28% of
KdPAR), while the chlorophyll containing particles accounted for approximately 14.24% of
KdPAR), and apparent color 7.35%. McPherson and Miller (1987), using samples collected
in Charlotte Harbor, Florida during 1984 and 1985 found on average that tripton accounted
for 72% of the total K/PAR), color accounted for 21%, and suspended chlorophyll accounted
for approximately 4%.
2.4.4 Analysis by Section
The same analysis performed on each of the data sets was also done for each of the
five sections of the IRL used in this study. The five divisions are a South section below
Northing UTM 3111063 m near Eau Gallie River, a Middle section between Northing UTM
3111063 m and Northing UTM 3154507 m just south of where state road 405 crosses the
IRL a North section above Northing UTM 3154507 m, Banana River, and Mosquito
Lagoon. The divisions were made to try to group sample sites according to like sections of
the lagoon and also to have enough data for analysis in each section. As seen in Table 2.22,
43
the results are very similar for each of the sections with tripton contributing the most to the
light attenuation coefficient, followed by color and the chlorophyll a.
Table 2.22: Percent of KdPAR) due to color, chlorophyll a, and tripton for each
section of the IRL.
Section % KdPAR) Due to % K(PAR) Due to % KdPAR) Due to
Color Chl_a Tripton
North 25.08 12.12 58.54
Middle 27.80 12.16 55.67
South 24.17 12.63 60.04
Banana
Banana 22.18 14.85 57.92
River
Mosquito 28.09 10.53 57.48
Lagoon
2.4.5 Analysis by Season
The same analysis was also done for each season in order to see if different
components had different influences at different times of year. The results are shown in
Table 2.23. Again, not much variation is seen between the different seasons. Two things
that are noticed, though, are that the average percentage of KdPAR) due to color goes down
as the year goes on and the average percentage of KdPAR) due to chlorophyll a increases
from the first half of the year to the second half of the year. Data from 1998 show an
increase in chlorophyll a during the fall (Chenxia Qiu, personal communication). In each
season, tripton again contributes the most to the total light attenuation, followed by color and
chlorophyll a.
Table 2.23: Percent of K/PAR) due to color, chlorophyll a, and tripton for each season.
Season % K(PAR) Due to % K(PAR) Due to % K/PAR) Due to
Color Chl_a Tripton
Jan. March 27.14 11.23 57.99
April June 25.10 11.04 59.39
July Sept. 24.35 15.27 56.89
Oct. Dec. 22.45 15.60 58.74
While the preceding analyses show relative contribution of each component to the
total KdPAR) for each data set, it must be remembered that they are approximations. It must
also be remembered that the values for tripton are calculated by subtracting the contributions
to KdPAR) from the other variables from the total K(PAR) from data. This, therefore, does
not come from the actual tripton data. Since tripton is closely related to TSS, these K,,ri may
not follow along well with TSS data either. An example of this may be seen by examining
the two different UF data sets. While the first six UF sampling trips have a mean TSS value
of 7.88 mg/L and the second six sampling trips have a mean TSS value of 30.58 mg/L, the
percentages of K(PAR)due to tripton in each data set are 60.10% and 49.94%, respectively.
This may show a little of two things. The first is that the mean color value for the second six
sampling trips is higher (22.46 Pt. Units, as opposed to 14.72 Pt. Units for the first six trips)
and therefore, using this method of analysis, leaves less K/PAR) to be associated with
tripton. While this may indicate a flaw in this analysis, it also goes against intuition. The
average chlorophyll a values for the two data sets are 5.26 gg/L for the first six sampling
trips and 7.22 lig/L for the second six sampling trips. These are very similar with the average
for the second six trips being slightly higher. Intuition would say that if the amounts of each
45
of the attenuators increase, so should the attenuation, but in this case the average light
attenuation coefficient for the first six trips is 1.02 m', while for the second six trips the light
attenuation coefficient is 0.97 m''.
2.5 Data Differences
Differences in data sets are inevitable, even when every precaution is taken to
minimize them. Each data set is being collected by different people who may have all been
taught the same exact techniques, but each may do things in slightly different ways when
confronted with the challenges of sampling in the field. Compounding the problem for this
task is not only different people in one group collected data, but different groups collected
data and different labs analyzed the data. Analysis of the processed data for each set showed
differences in the data, particularly total suspended solids (TSS). Some of the most obvious
differences occurred between UF synoptic trips 16 and UF synoptic trips 712, as well as
between WQMN data sampled before and after March, 1999. The two years of HBOI
sampling also showed higher TSS values, but do not have a source for comparison as the UF
and WQMN data do. Since our goal was to use as much of the available data as possible,
ways were sought to adjust for these differences.
Since the IRL is a shallow estuary, resuspended sediment would be expected to
increase during wind events (Sheng et al., 1992). Suspended sediment would also be
expected to be a main cause of light attenuation (McPherson and Miller, 1987; Phlips et al.,
1994). Therefore, K/PAR) would be expected to show a positive correlation with TSS.
Accordingly, higher TSS values would be expected to correspond with higher K/PAR)
values. This was not found to be the case when comparing different data sets, particularly
when comparing WQMN data collected between 19961998 to WQMN data collected in
46
1999, and also UF data collected in the first six synoptic trips to UF data collected during the
second six synoptic trips. While WQMN 1999 data and UF trips 712 data contained much
higher TSS numbers than the previous sampling by each group had shown, the average
K/PAR) values were not appreciably higher, which runs counter to expectations.
2.5.1 UF Data
As stated in the previous section, the average KdPAR) value for UF's second six
sampling trips is less than that for the first six sampling trips, despite a higher average TSS
value. The regressions for KdPAR) against TSS for the UF sampling trips 712, while very
poor with R2=0.0013, does show a negative relationship for KdPAR) against TSS, as shown
in Equation 2.3.
Kd (PAR) = 0.001 TSS + 0.9968 (R2 = 0.0013) (2.3)
UF sampling trips 16 show a positive correlation between K(PAR) and TSS as seen in
Equation 2.4.
Kd(PAR) = 0.0619 TSS + 0.5309 (R2 = 0.40) (2.4)
The graphs of K/PAR) against TSS for both of these data sets are seen in Figures 2.4
and 2.5. To better illustrate the differences between the two data sets, the average TSS value
for UF sampling trips 712 (TSS = 30.58 mg/L) is used in the regression for K(PAR) from
UF sampling trips 16. The result is a predicted K(PAR) of 2.42 mn, while the average
K/PAR) for the second six sampling trips is only 0.97 m"1. The result of using the UF 712
average TSS value in the equation for sampling trips 712 is the same KdPAR) as the average
of 0.97 m'. This illustrates that if the regression relationship for sampling trips 16 is
47
correct, then the K/PAR) values for sampling trips 712 should be higher according to the
corresponding TSS values.
2.5.2 WOMN Data
The same discrepancies between TSS K(PAR) equations are seen in the WQMN
data sets, even though the R2 values for the regressions are not as high. While the regression
for K/PAR) against TSS for WQMN 1999 does not have a negative correlation, it does have
a much gentler slope than the regression for WQMN 19961998. This is seen in Figures 2.4
and 2.5, where the regression equation for WQMN 19961998 is:
Kd (PAR) = 0.0282 TSS + 0.7299 (R2 = 0.22) (2.5)
5.00_________________
.0 y = 0.0619x + 0.5309
R2= 0.3994
4.00
,*3.00
00 ... %
1. 50
1.00 
0.50 
0.00 .. .....
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
TSS (mg/I)
Figure 2.4: UF sampling trips 16 relationship between Kd(PAR) and TSS.
5.00
4.50
4.00
3.50
.3.00
M 2.50
M 2.00
S1.50
1.00
0.50
fA nf
y = 0.001x + 0.9968
R2= 0.0013
   ="""".,
U U
.UUJ i I I I I
0.00 20.00 40.00 60.00 80.00 100.00
TSS (mg/I)
Figure 2.5: UF sampling trips 712 relationship between Kd(PAR) and TSS.
and the regression equation for WQMN 1999 is :
Kd (PAR) = 0.0053 + 0.9472 (R2 = 0.0529) (2.6)
If the average TSS value for WQMN 1999 (TSS = 62.96 mg/L) is used in the WQMN
19961998 equation, it predicts a K(PAR) of 2.51 m1, compared to an average K(PAR) for
WQMN 1999 data of 1.28 m'. If the average WQMN 1999 TSS value is used in the
WQMN 1999 equation, it predicts the average KIPAR) of 1.28 mi'.
The Turbidity and TSS relationships should also be examined here to see if they
match up well for the WQMN data sets. Figures 2.8 and 2.9 show the relationships for
WQMN 19961998 and WQMN 1999, respectively. The regression equation for WQMN
19961998 is:
Turbidity = 0.3427 TSS + 1.0217 (R2 = 0.6769) (2.7)
while the regression equation for WQMN 1999 is:
Turbidity = 0.1148 TSS + 2.0551 (R2 = 0.3442). (2.8)
As for the TSS relationships with K(PAR), there are differences between the
Turbidity TSS relationships of each data set. The slope for the WQMN 1999 regression
is about a third of what it is for the WQMN 19961998 data set. This means that as the TSS
values increase, the 19961998 data indicate a much higher turbidity than the 1999 data
indicate. So, if a TSS value of 50 mg/L is used in both of those equations, the 19961998
equation predicts a turbidity value of 18.16 NTU's, while the 1999 equation predicts a
turbidity value of 7.80 NTU's. Turbidity was not measured during the UF sampling trips
so this type of comparison can not be done for those data sets.
5.00
y = 0.028
4.50
4.00
3.00
S2.50 
2.00 .
E
0.50I
1.00 ME
0.00
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00
TSS (mg/I)
Figure 2.6: WQMN 19961998 relationship between Kd(PAR) and TSS.
90.00 100.00
5.00
4.50
4.00
^3.50
1,3.00
C 2.50
0 2.00
S1.50
1.00
0.50
0.00
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00
TSS (mg/L)
Figure 2.7: WQMN 1999 relationship between Kd(PAR) and TSS.
90.00 100.00
90.00 
y = 0.3427x + 1.0217
80.00 R2=0.6769
70.00
p 60.00
Z
50.00
0 40.00 
30.00 .
20.0 0 
10.00 *N7 1
0.00 "
0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00
TSS (mg/L)
Figure 2.8: WQMN 19961998 relationship between turbidity and TSS.
160.00
y = 0.0053x + 0.9472
R2= 0.0529
U U_ U
 F. U i 
 
90.00
80.00 = 0.1148x + 2.0551
2 = 0.3442
70.00
60.00
I
Z
50.00
"0 40.00
30.00
20.00 _
0.00
0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 180.00 200.00
TSS (mg/L)
Figure 2.9: WQMN 1999 relationship between turbidity and TSS.
2.5.3 HBOIData
Both years of sampling by HBOI show relatively high average TSS values with the
average TSS for HBOI Year 1 being 57.01 mg/L and the average for HBOI Year 2 being
67.43 mg/L. The average K/PAR) values are also higher than for the other data sets with
the average K/PAR) for HBOI Year 1 being 1.67 m' and the average for HBOI Year 2 being
1.76 m' To see if these numbers are consistent with any of the trends seen in the other data
sets, the average TSS values for HBOI Years 1 and 2 are used in the K(PAR) TSS and
TurbidityTSS regression equations of the other data sets. The regression equations for
KdPAR) TSS and Turbidity TSS for HBOI Year 1 are shown in Equations 2.9 and 2.10,
with the graphs being shown in Figures 2.10 and 2.11.
Kd (PAR) = 0.0201* TSS + 0.5057 (R2 = 0.1806) (2.9)
Turbidity = 0.1916 TSS 4.0611 (R2 = 0.5685) (2.10)
52
The regression equations for HBOI Year 2 are shown in Equations 2.11 and 2.12. The
graphs of the relationships are shown in Figures 2.12 and 2.13.
Kd (PAR) = 0.0044 TSS + 1.462 (R2 = 0.0095) (2.11)
Turbidity = 0.1151* TSS + 0.5324 (R2 = 0.2114) (2.12)
The results using average HBOI TSS values in each of the regression equations are
shown in Tables 2.24 and 2.25.
As is seen in Table 2.25, the predictions for K(PAR) using the average TSS
values for HBOI Years 1 and 2 in the K(PAR) TSS regression equation for each data set
7.00 . ...... ......... .... .. .. .....  ..........
0 = 0.0201 x + 0.5057
6.00 R= 0.1806
^5.00
V4.00
2X 3.00 *  " " ,
13.00 U.
0.00 I
0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 180.00 200.00
TSS (mg/L)
Figure 2.10: HBOI year 1 relationship between Kd(PAR) and TSS.
5 0 .0 0 ..... ....................... ............................ ........... .
45.00 y=0.1916x 4.0611 q
R2 = 0.5685
40.00
s35.00
Z30.00
.25.00
20.00
015.00 
I I
10.00 U U no ut 
5.00 " ,'' i I mI
0.00 ...i
0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 180.00 200.00
TSS (mg/L)
Figure 2.11: HBOI year 1 relationship between turbidity and TSS.
7.00
y = 0.0044x + 1.462
6.00
00 R2 = 0.0095
S5.00
IN I U *
2.00 4"1 IN* *
1.00
IN l U U
0.00 U"
0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 180.00
TSS (mg/L)
Figure 2.12: HBOI year 2 relationship between Kd(PAR) and TSS.
50.00
45.00
40.00
'35.00
I.
Z 30.00
=25.00
20.00
115.00
I
10.00
5.00
0.00
y =O1151x + 0.5324
R = 0.2114
FAS
%A
U
yl + ,'
U U U
E
:E
0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 180.00 200.00
TSS (mg/L)
Figure 2.13: HBOI year 2 relationship between turbidity and TSS.
Table 2.24: Turbidity calculations using HBOI years 1 and 2 average TSS values.
Data Set HBOI Year 1 HBOI Year 2 WQMN 9698 WQMN 1999
HBOI Year 1 6.86 7.09 22.56 8.60
HBOI Year 2 8.86 8.29 24.13 9.80
Table 2.25: K(PAR) calculations using HBOI years 1 and 2 average TSS values.
Data Set HBOI HBOI WQMN WQMN UF 16 UF 712
Year 1 Year 2 199698 1999
HBOI
a 1.65 1.71 2.34 1.25 4.06 0.94
Year 1
HBOI
HBa 1.86 1.76 2.63 1.30 4.70 0.93
Year 2
55
vary greatly. The average K/PAR) value for each HBOI data set is best predicted by the
K/PAR) TSS regression equation for that data set. The K/PAR) TSS equations from the
WQMN 19961998 and UF 16 data sets, the data sets with lower TSS values, overpredict
the average K/PAR) for the HBOI data, while WQMN 1999 and UF 712, the data sets with
higher TSS values, underpredict. This indicates that there are major differences between the
data sets which could cause problems when trying to model all of the data sets at once.
2.5.4 Attempt to Make TSS Data Uniform
The one similarity for both the WQMN and UF data sets is a change of labs for
sample analysis occurred between the separation of data for both sets. One lab did the
analysis for WQMN 19961998 and the first six UF sampling trips. Another lab did the
analysis for WQMN 1999 and the second six UF trips2. If it can be assumed that sampling
methods and techniques used by both groups remained the same between sampling trips, then
a closer look at the labs used for sample analysis should be taken.
Split sample analysis was done in order to try and determine if there were differences
between the analyses done by the two labs. Samples were taken at the northern UF inshore
sampling tower at 280 39' 18.36" N latitude and 800 48' 4.02" W longitude at 14:00 EST on
13 April 2000. The samples were taken in a Niskin type bottle at 20% and 80% of the total
depth. One sample for each lab was taken out of the same Niskin bottle sampling with care
being taken to assure uniformity between the samples. Two samples from the upper location
2The changing of labs occurred after UF sampling trip number 6 for the UF data. For the WQMN data the
change took place in October of 1998. While the WQMN data does not show an increase through the end of 1998,
the first data used in 1999 was in March. The reason the jump did not occur in WQMN data for October through
December 1998 is not known.
56
and two from the lower location were each sent to each of the labs. The results are shown
in Table 2.26.
Table 2.26: Results from TSS split sample analysis.
Laboratory Upper Level TSS Value (mg/L) Lower Level TSS Value (mg/L)
Lab 1 17.4 15.8
Lab 2 135.0 36.2
The results for the lower samples are somewhat similar, but the initial results for the
upper samples are extremely different with the number from the second lab being extremely
high. This was brought to the attention of the second lab and the results from the first lab
were revealed. The second lab then redid their calculations and presented a corrected value
of 17.8 mg/L. When asked to see what was done, we did not get a detailed account from the
second lab, but instead a description of what should have been done.
Since these discrepancies did exist, any model which used TSS as an input to try to
predict KdPAR) values would not be able to be calibrated to both of these extremes (an
explanation of the models will appear later). An attempt needed to be made to find a
relationship between the TSS values found by both labs in order to try to convert all of the
TSS data to resemble that of one lab. Since the TSS reported by the first lab had a better
correlation with KdPAR), the numerical model (which will be explained later) was calibrated
using TSS numbers which resemble the first lab results, and there are more data resembling
that from the first lab, it was decided to try to find a way to convert the data from the second
lab to resemble that of the first.
57
The common thread which was found to do this is the turbidity measurements for the
WQMN data. Turbidity data are also analyzed by the labs, but we do not have reason to
suspect major differences in the methods used by the two labs. Therefore, the Turbidity 
TSS relationships shown in Figures 2.8 and 2.9 are used for the conversion. The TSS
numbers for UF synoptic sampling trips 712 as well as WQMN 1999 are converted to
turbidity using the Turbidity TSS relationship for WQMN 1999 data (Eq. 2.8). These
"turbidity" numbers were then used in the rearranged WQMN 1996 1998 Turbidity TSS
relationship to find the converted TSS values.
(Turbidity 1.0217)
TSS = (2.13)
0.3427
Since the two HBOI data sets also contain high TSS values, the same conversion method
is used in order to make the TSS data more uniform for easier use in the numerical model.
2.6 Data Sets Statistics With Converted TSS Values
This section shows the TSS statistics for the data sets with the high original TSS
values after the conversion using the TSSTurbidity relationships from WQMN 19961998
and WQMN 1999. It also shows the data statistics, including the converted TSS values for
each season and also for the five different sections of the IRL used in this analysis.
2.6.1 Converted TSS Data Sets
The statistics for the converted TSS values are shown in Table 2.27. The other
variables are not shown because they did not change. Table 2.28 shows a comparison
between the original and converted TSS values for each data set. The mean TSS values for
UF sampling trips 712, WQMN 1999, HBOI Year 1, and HBOI Year 2 decrease between
58
the original and converted TSS values by 56.64%, 61.72%, 61.21%, and 62.03%,
respectively.
Table 2.27: Transformed TSS statistics using WQMN 19941998 and WQMN 1999
turbidityTSS relationships;
Data Set Minimum TSS Maximum TSS Mean TSS Standard Deviation
(mg/L) (mg/L) (mg/L) (mg/L)
UF 712 6.11 43.38 13.26 5.47
WQMN 7.57 48.24 24.10 8.86
1999
HBOI 1 3.02 70.01 22.11 9.00
HBOI 2 11.06 56.38 25.60 8.05
2.6.2 Seasons Statistics
All of the data sets are combined for use in the data sets for each season. The seasons
are divided into four three month data sets. The first division is January March,the second
one is April June, the third is July September, and the fourth is October December. The
statistics for each of these are shown in Tables 2.29 through 2.32.
Examining the mean values, chlorophyll a has the lowest mean concentration during
April June at 6.66 Vg/L and the highest average concentration of 15.32 pg/L during
October December. Color has its lowest mean value of 15.95 Pt. Units during April June
and its highest mean value of 24.76 Pt. Units during October December. The lowest mean
TSS concentration of 14.42 mg/L comes during April June and the highest mean TSS
concentration of 18.46 mg/L comes during October December. As would be expected,
April June, which has the lowest mean values of the other variables, also has the lowest
59
K/(PAR) value of 1.09 m'. Along those same lines, October December has the highest
mean values for each of the variables and also the highest mean value of KdPAR) of
1.60 m'.
Table 2.28: TSS (mg/L) statistics for data transformed using WQMN 19941998 and
WQMN 1999 turbidityTSS relationships.
Data Set Minimum TSS Maximum TSS Mean TSS Standard Deviation
UF 712
UF 72 9.24 120.50 30.58 16.34
Original
UF 712
U e72 6.11 43.38 13.26 5.47
Converted
WQMN
1999 13.60 135.00 62.96 26.46
Original
WQMN
1999 7.57 48.24 24.10 8.86
Converted
HBOI 1
HBO1 0.01 199.99 57.00 26.86
Original
HBOI 1
o 3.02 70.01 22.11 9.00
Converted
HBOI 2
Ori 24.01 159.30 67.42 24.02
Original
HBOI 2
HBo2 11.06 56.38 25.60 8.05
Converted
2.6.3 Sections Statistics
The statistics for each of the sections of the IRL are presented here to see if any
noticeable differences are present. This information may be important later for calibration of
the numerical light attenuation model. The statistics are shown in Tables 2.33 through 2.37.
60
For the sections, Mosquito Lagoon has the highest TSS mean value with 23.65 mg/L
while Banana River has the lowest mean TSS value of 13.43 mg/L. Chlorophyll a
concentration is the highest in the South Section with a mean value of 12.39 pg/L and is the
lowest in the Middle Section with a mean value of 7.23 lg/L. For Color, the highest mean
value occurs in the South Section with a value of 25.02 Pt. Units and the lowest mean value
occurs in the Middle Section with a value of 13.43 Pt. Units. As for the K/PAR) values, the
highest mean value is 1.60 m1 for the South Section which has the highest mean values for
color and chlorophyll a. It also has the second highest mean TSS value of 19.37 mg/L. The
lowest mean K/PAR) value is 0.94 m' in the Banana River. The only other variable with the
lowest mean value being in the Banana River is color.
Table 2.29: Statistics for January March with transformed TSS values.
Variable Minimum Maximum Mean Standard
Deviation
TSS (mg/L) < 5.00 70.01 16.54 10.97
Chlorophyll a ([pg/L) 1.11 50.55 9.33 7.70
Color (Pt. Units) < 7.00 94.00 21.87 15.41
Kd(PAR) (m1) 0.09 6.84 1.40 1.04
Table 2.30: Statistics for April June with transformed TSS.
Variable Minimum Maximum Mean Standard
Deviation
TSS (mg/L) < 5.00 89.50 14.42 10.81
Chlorophyll a (pg/L) < 1.00 37.22 6.66 4.98
Color (Pt. Units) <7.00 69.90 15.95 7.93
Kd(PAR) (m') 0.05 4.62 1.09 0.65
Table 2.31: Statistics for July September with transformed TSS.
Variable Minimum Maximum Mean Standard
Deviation
TSS (mg/L) < 5.00 43.20 17.92 9.62
Chlorophyll a (pg/L) < 1.00 68.57 13.36 11.00
Color (Pt. Units) < 7.00 103.60 23.53 17.95
Kd(PAR) (m1) 0.33 6.88 1.45 0.90
Table 2.32: Statistics for October December with transformed TSS.
Variable Minimum Maximum Mean Standard
Deviation
TSS (mg/L) < 5.00 43.38 18.46 8.02
Chlorophyll a (pig/L) 1.81 96.22 15.32 13.80
Color (Pt. Units) <7.00 165.60 24.76 22.24
Kd(PAR) (m') 0.04 6.59 1.60 1.05
Table 2.33: Statistics for the South Section of the IRL with transformed TSS.
Variable Minimum Maximum Mean Standard
Deviation
TSS (mg/L) < 5.00 70.01 19.37 10.98
Chlorophyll a (pg/L) < 1.00 96.22 12.39 11.09
Color (Pt. Units) < 7.00 165.60 25.02 20.49
Kd(PAR) (m') 0.04 6.88 1.60 1.01
Table 2.34: Statistics for the Middle Section of the IRL with transformed TSS.
Variable Minimum Maximum Mean Standard
Deviation
TSS (mg/L) < 5.00 49.00 9.73 7.33
Chlorophyll a ([g/L) < 1.00 35.01 7.23 4.97
Color (Pt. Units) 7.50 70.00 18.22 8.16
Kd(PAR) (m1) 0.33 3.71 1.00 0.46
Table 2.35: Statistics for the North Section of the IRL with transformed TSS.
Variable Minimum Maximum Mean Standard
Deviation
TSS (mg/L) < 5.00 55.00 14.74 8.91
Chlorophyll a (l[g/L) < 1.00 68.57 8.96 8.80
Color (Pt. Units) < 7.00 90.00 16.51 9.41
Kd(PAR) (m') 0.05 6.43 1.23 0.88
Table 2.36: Statistics for the Banana River with transformed TSS.
Variable Minimum Maximum Mean Standard
Deviation
TSS (mg/L) < 5.00 37.90 16.56 7.39
Chlorophyll a (ig/L) < 1.00 79.09 8.36 9.32
Color (Pt. Units) < 7.00 52.00 13.43 6.41
Kd(PAR) (m') 0.09 6.22 0.94 0.64
Table 2.37: Statistics for the Mosquito Lagoon with transformed TSS.
Variable Minimum Maximum Mean Standard
Deviation
TSS (mg/L) 6.60 89.50 23.65 15.99
Chlorophyll a (pg/L) 1.58 22.90 7.95 6.14
Color (Pt. Units) 11.00 45.00 21.27 8.21
Kd(PAR) (m1) 0.43 3.16 1.28 0.66
CHAPTER 3
REGRESSION MODELS
3.1 Introduction
One way to try to find a light attenuation model is to find a simple regression
relationship between the Kd(PAR) calculated from light measurements and the water quality
measurements taken simultaneously. This type of empirical model is a simple way to relate
light attenuation to water quality at a certain time. This method was used previously by
McPherson and Miller (1994) in Tampa Bay and Charlotte Harbor.
The water quality parameters used for the regression analysis are total suspended
solids (TSS), chlorophyll a (chl_a), and color. The chlorophyll a concentration is related to
the phytoplankton concentration in the water while the color in the water is related to
dissolved organic matter within the water. These parameters are chosen for three main
reasons. The first is that they are all known light attenuators (Gallegos, 1993). The second
is that they are the same parameters used in the numerical light attenuation model which is
being tested. This enables an easier comparison between the models. The third reason is that
they are recognized as actual light attenuators. An example of the opposite of this would be
using salinity in a light attenuation model for highly colored water coming from a freshwater
source. Here, salinity may be very well correlated with light attenuation, but the color in the
water is what is doing the attenuating, not the salinity. McPherson and Miller (1994) found
a relationship between the light attenuation coefficient and salinity to have a r? = 0.71 in
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Tampa Bay and Charlotte Harbor, but note that the increase in attenuation comes from an
increase in color, suspended matter, and nutrients causing algal growth.
Using those three parameters, the best onevariable, twovariable, and threevariable
linear stepwise regression models are produced for each of the available data sets using the
PROC REG option available in SAS software (SAS Institute Inc, 1990). Using the stepwise
method means that just because a variable is used in the onevariable model, it does not
necessarily need to be used in the twovariable model, thus allowing for the best model to
be found. In addition, a threevariable, nonlinear factorial regression model is also
produced for each data set using the PROC GLM option in SAS software. Whereas the
simple regression models have one coefficient for each variable, as well as an intercept, the
factorial model also includes coefficients for products of the variables. Each model also
includes an R2 value to help judge the fit as well as a p value in order to measure the
significance of each component in the model.
In addition to finding the models for each of the data sets separately, linear regression
and factorial models have been developed for all of the available data together at once. The
combined data were then divided into seasons and sections of the IRL to see if time or space
dependent models would provide better results. Not enough data were available to divide
each separate data set into seasons and sections. The seasonal divisions are January March,
April June, July September, and October December. The sections of the lagoon used
include Banana River, Mosquito Lagoon, a southern section up to Northing UTM 3111063 m
near Eau Gallie River, a middle section between Northing UTM 3111063 m and Northing
UTM 3154507 mjust south of where state road 405 crosses the IRL, and a northern section
north of Northing UTM 3154507 m.
3.2 Regression Model Statistics
In order to understand the analysis used in this chapter, a few terms need to be
defined. The "fit" of the regression model to the data is determined using the coefficient of
determination, r. For a linear regression model using one independent variable and one
dependent variable, r2 indicates the percentage of the total sums of squares that is fit by the
regression model (Weimer, 1987). Weimer (1987) gives a good explanation of just what this
means and how it is calculated.
To see if the regression model that has been calculated is dependable enough to be
used for modeling the dependent variable, a hypothesis needs to be tested. The hypothesis
tested is known as the null hypothesis, Ho. Weimer (1987) defines the null hypothesis as the
hypothesis of "no difference." The null hypothesis for this study is that the model does not
predict KPAR. So for the regression equation in Equation 3.1:
1 = bo + bx (3.1)
the null hypothesis would be that b, = 0 and therefore
5 = bo (3.2).
If this is the case, then each answer for y is bo, no matter what values x is, so x makes "no
difference." If this is the case, then we say:
Y = bo (3.3)
So then we have three different values for y: the observed value, y, the value
calculated by the regression equation, and the result of the null hypothesis, y There is
a deviation between y and y This can be partitioned into the difference between 5 and y,
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which is the deviation due to the regression, and the difference between y and y which is
the deviation due to error. This is shown in equation 3.4.
y y = (y ) ( y) (3.4)
The sum of the squares of each component satisfies:
S(Y = (Y )+ )2 (3.5)
where:
sum of squares of y (SSy) = (y y)2 (3.6)
sum of squares for error (SSE) = (y )2 (3.7)
sum of squares for regression (SSR) = ( y)2 (3.8).
Using the above definitions, r2 is defined in:
r2 = SSR/SSy (3.9).
The r2 is used to denote the coefficient of determination since it can be shown to be
the square of the Pearson correlation coefficient, r (Weimer, 1987). A Pearson correlation
coefficient with a value of 0.60 is being taken here to indicate real world significance
(Kornick, 1998). This correlates with a r2 of 0.36. For the cases when more than one
variable is used in the regression equation, the multiple correlation coefficient R2 is used.
In the case of this paper, R2 is used to denote the correlation coefficient for each regression
model, therefore keeping with the same notation as the SAS output.
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An F distribution is used to determine if the model and each variable in the model are
statistically significant. In order to use an F distribution, first an F statistic must be
calculated. For the regression model, an F statistic is calculated with:
SSR
F 2 (3.10)
Se
where SSR is defined in equation 3.8 and S2 the residual variance, is defined in:
S SSE
s2 (3.11).
e n 2
where SSE is defined in equation 3.7 and n is the number of points.
The degrees of freedom for the numerator and denominator of Equation 3.10 are
needed since the F distribution is dependent upon degrees of freedom in its constituents. By
definition, the degree of freedom in the numerator is one. The degrees of freedom for the
denominator are n 2. The degrees of freedom as well as the F statistic are then used to find
a probability value (p value) for the model. This p value, when compared to a level of
significance (a) is used to determine if the null hypothesis can be rejected or not. Weimer
(1987) defines the p value as "the smallest level of significance that would have resulted in
Ho being rejected." If the p value is less than a (in this case 0.05), then the null hypothesis
can be rejected and the model is statistically significant.
An F statistic is also calculated for each added variable with Equation 3.12 to see if
the null hypothesis can be rejected for each variable.
AR2/g
F A (3.12)
(1 R2)1(n k 1)
In Equation 3.12, AR2 is the change in R2 with the addition of the new variable, g is the
number of new variables added, n is the number of points, k is the total number of variables
used (Wonnacott and Wonnacott, 1977). In this equation, g are the degrees of freedom in
the numerator and n k 1 are the degrees of freedom in the denominator. These are used
to find ap value the same way as they are for the F statistic for the entire model.
In general, the larger the F statistic is, the smaller the p value is, and therefore the
chances are better of having the model or variable be statistically significant. Because of the
position of the total number of samples, n, in the equations, it can be seen that larger values
of n lead to larger values of F statistics. Therefore, larger data sets have a better opportunity
of having the variables and regression model be statistically significant.
3.3 Regression Models for Various Data Sets
In this section the best one, two, and three variable stepwise regression models as
well as the best three variable factorial model are presented for each individual data set and
for the combined data set. This allows for comparison to see how compatible a model for
one data set may be with another data set.
3.3.1 Best OneVariable Linear Regression Model for Each Data Set
The results for the best one variable model for each data set are shown in Table 3.1. Many
things can be seen just by looking at the results for the best onevariable model. The first,
by looking at the R2 values, is that the SERC data set has the best fitting onevariable model
with R2=0.6824. The best onevariable model for this data set uses color as the variable.
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This makes sense in that one of the goals of Gallegos using this data set (Gallegos, 1993) was
to be able to investigate the effects of color on light attenuation modeling. Also, this data
set included sampling at Turkey Creek, where a color lens was found on the surface of the
water and was attempted to be modeled. All of the onevariable models for the other data
sets, including the combination of all of the data, are statistically significant to the 0.05 level
except WQMN 1999 and Phlips which are very small data sets (Table 3.2). Of the data sets
in which the TSS values were highest (Harbor Branch Year 1, Harbor Branch Year 2, UF
Trips 712, and WQMN 1999) HBOI Year 2 and UF Trips 712 do not have TSS as the best
one variable model, but instead use color and chlorophyll a, respectively. Also, even though
only UF Trips 712 has chlorophyll a in the model, and five of the eight separate data sets
have TSS, the combination of all of the data sets has a one variable model with chlorophyll
a.
Table 3.1: Best onevariable regression model for each data set.
Data Set Coefficient and Variable Intercept R2
All Sets 0.04085 chl_a 0.90280 0.1935
HBOI Year 1 0.06132 tss 0.31317 0.1776
HBOI Year 2 0.02117 color 1.34719 0.1499
UF Trips 16 0.06187 tss 0.53106 0.3994
UF Trips 712 0.03594 chl_a 0.70714 0.1492
WQMN 19961998 0.02823 tss 0.72991 0.2179
WQMN 1999 0.01610 tss 0.89213 0.0662
Phlips 0.03310 tss 1.07845 0.0838
SERC 0.01479 color 0.88387 0.6824
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Perhaps the best point that can be made from these results is the variation between
data sets, not only variation in the variables used for each data set's model, but also the
variation between equations in which the same variable is used. This agrees with Kornick's
(1998) findings. Since there is such variation in variables used, we must add another variable
to see if there is an improvement.
Table 3.2: F values and p values for the best onevariable regression models.
Data Set Variable F Value p Value
All Sets Chl_a 302.70 < 0.0001
HBOI Year 1 TSS 35.41 < 0.0001
HBOI Year 2 Color 52.38 < 0.0001
UF Trips 16 TSS 158.24 < 0.0001
UF Trips 712 Chl_a 24.02 < 0.0001
WQMN 19961998 TSS 88.05 < 0.0001
WQMN 1999 TSS 1.98 0.1699
Phlips TSS 1.55 0.2294
SERC Color 109.60 < 0.0001
3.3.2 Best TwoVariable Linear Regression Model for Each Data Set
By adding a second variable to the regression models, the R2 values improve for all
of the data sets as shown in Table 3.3. Again, neither of the variables used in the models for
the Phlips data set nor for the WQMN 1999 data set are statistically significant at the 0.05
level. This is due, at least in part, to the small sizes of each of those two data sets.
As shown in Table 3.4, another interesting note is that the two variable regression
model for all of the data sets combined uses TSS and color (both of which are more
statistically significant with p values of <0.0001), while chlorophyll a is used in the one
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variable model and is statistically significant at the 0.05 level in that model with ap value
of <0.0001.
Table 3.3: Best twovariable model for each data set.
Data Set Coefficient Coefficient Intercept R2 R2
and Variable and Variable Improvement
All Sets 0.04153 tss 0.02058 color 0.22263 0.3135 0.1200
HBOI
HB1 0.077041 tss 0.03235 color 0.60507 0.3822 0.2046
Year I
HBOI
HBOI 0.01822 color 0.02807 chl_a 0.93994 0.2459 0.0960
Year 2
UF
S1 0.05431 tss 0.04812 chla 0.33744 0.4394 0.0400
Trips 16
UF
S 0.01135 color 0.03681 chlia 0.44584 0.2753 0.1261
Trips 712
WQMN 0.02594 tss 0.01649 color 0.35790 0.3592 0.1413
19961998
WQMN 0.02081 tss 0.04235 chl_a 0.52962 0.1144 0.0482
1999
Phlips 0.04447 tss 0.03593 color 0.19068 0.1297 0.0459
SERC 0.01495 color 0.01715 chl_a 0.77365 0.7375 0.0551
Using an R2 of 0.36 to determine if the regression model has real world significance,
the two variable models for HBOI Year 1, UF Trips 16, and SERC all fit that criterion. In
order to see if any more data sets can have models which fit this criterion, a third variable is
added.
3.3.3 Best ThreeVariable Linear Regression Model for Each Data Set
Table 3.5 shows the best three variable linear regression model for each of the data
sets. Again, the addition of another variable improves the R2 of the models for each data set,
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with the combined data set improving the most (0.0539 to R2 = 0.3674), while others barely
improve at all over the twovariable models (UF Trips 16 up only 0.0017 to R2 =
Table 3.4: F values andp values for the best twovariable regression models.
Data Set Variable F Value p Value
All Sets TSS 415.32 < 0.0001
Color 230.79 < 0.0001
HBOI Year 1 TSS 69.97 < 0.0001
Color 53.98 < 0.0001
HBOI Year 2 Color 42.31 < 0.0001
Chl_a 37.66 < 0.0001
UF Trips 16 TSS 113.22 < 0.0001
Chl_a 16.93 < 0.0001
UF Trips 712 Color 23.68 < 0.0001
Chl_a 29.36 < 0.0001
WQMN 19961998 TSS 89.55 < 0.0001
Color 69.47 < 0.0001
WQMN 1999 TSS 3.02 0.0938
Chl_a 1.47 0.2357
Phlips TSS 2.29 0.1499
Color 0.85 0.3715
SERC Color 132.64 < 0.0001
Chl_a 10.49 0.0021
0.4411) (Table 3.6). With three variables, the models for the combined data set, HBOI
Year 1, UF Trips 16, WQMN 19961998, and SERC all have R2 values indicating real world
significance with SERC again having the highest R2 value with R2 = 0.7618.
Since the third variable is prescribed and not chosen from a pool of variables to give
the best fit for the model, the third variable in many of the data sets ends up being
statistically insignificant at the 0.05 level. This, as shown in Table 3.7, is the case for both
UF data sets. All three of the variables for WQMN 1999 and Phlips showed no statistical
significance at the 0.05 level.
Table 3.5: Best threevariable regression model for each data set.
Data Coefficient for Coefficient for Coefficient for Intercept
Set TSS Color Chl_a
All Sets 0.03275 0.01774 0.02373 0.18468
HBOI Year 1 0.07300 0.03110 0.00639 0.57740
HBOI Year 2 0.02774 0.02176 0.02656 0.18644
UF Trips 16 0.05400 0.00831 0.04914 0.45681
UF Trips 712 0.01064 0.01268 0.03810 0.26555
WQMN 19961998 0.02544 0.01458 0.00932 0.33958
WQMN 1999 0.02163 0.00281 0.04136 0.45431
Phlips 0.04421 0.03498 0.00463 0.29913
SERC 0.01675 0.01632 0.01377 0.57898
Table 3.6: R2 values for the best threevariable model for each data
set and the improvement in R2 over the two variable model.
Data Set R2 R2 Improvement
All Sets 0.3674 0.0539
HBOI Year 1 0.3851 0.0029
HBOI Year 2 0.2849 0.0390
UF Trips 16 0.4411 0.0017
UF Trips 712 0.2904 0.0151
WQMN 19961998 0.3703 0.0111
WQMN 1999 0.1160 0.0016
Phlips 0.1310 0.0013
SERC 0.7618 0.0243
